Welp, For Scott's sake and mine I might as well take a shot at answering the riddle he's made for us...
FNAF 4, like its counterparts had mini-games involving 8-bit representations of past events, and solving them aided in telling the story of the cursed pizza place. In the first three, it was obvious that the guy we're all playing as wasn't the same as those we play during the minigames. But here, because of the fact both are children, or at least assumed to be, we're thinking that the player is the little boy that went through such trauma while alive.
My theory begins with the thought that it isn't the little boy we're playing as, but his BROTHER. We have no sense of when these nightmares are taking place, so it's possible that they are occurring after the Bite of '87. Even if the older brother was as young as 8-9 years old, he would easily grasp the fact that his younger brother is dead, a character that the older brother thought was perfectly safe nonchalantly bit a chunk out of his kid brother's brain, and that it was the older brother's fault. Guilt does the rest after the younger brother dies, leaving the older brother plagued with nightmares of the animatronics now coming for him.
(Yes, there's that little bit with the TV showing 1983 along with the show Fred Fazbear and Friends, but keep this in mind. Copyrights usually only list the year the copyright was first established, so odds are that 1983 was the year Fred Fazbear came into public existence, and not the current year in question.)
This is further supported by the random objects that appear in the child's room as well as the room's composition during the game as well as the existence of Foxy. The little boy's room only has one door, whereas the room we have as the stage contains two. Secondly, the bed of the little boy in the minigame is flush with the corner of one of the walls, but in the main game this bed is in the middle of the far wall between both sets of doors. Now true, given that it's 8-bit in the mini games, the level of detail would be lessened considerably, but for broad things like the orientation of the walls and doors they'd be as accurate as possible. Furthermore, it's assumed that the little boy is in a coma, a type of deep sleep that isn't easy to wake from. So the flowers, pill bottle, IV bag, NONE of these things would have any reason to appear in the dreamstate since the boy hasn't seen any of these things the entire five nights. But for the older brother, who I would assume would visit every day, he'd see these things and incorporate them accordingly. Also, the inner workings of the animatronics are noticeable on all the nightmare forms, and in the third-fourth minigame we see that the older brother knows about the parts room in the restaurant, since he locked the little boy inside it. Doesn't seem impossible for him to make the connection between the parts and finished models. He just couldn't grasp that they might have that kind of crushing power when in motion.
Speaking of the animatronics, Foxy is further proof that we're working with the older brother and not the younger. In the very first mini game we see the little boy's room with all his little 'friends'. But notice: the Foxy doll has been decapitated in some way! And it makes sense why, the older brother loves Foxy, wearing the mask to scare the pants off of the little boy. Odds are the little boy tore up the Foxy doll as a form of revenge. But why might this matter? In the game, if you shut the door on Foxy enough times, it turns into a doll. But this one has his head. Why would the little boy, who went to all the trouble to destroy the Foxy doll and leave it that way, dream of Foxy in his complete form? He wouldn't, but the older brother might.
Now here is where I tie everything together with the other games since I've established my case that the player is the older brother instead of the little boy. Keep in mind, this part is wholly Wild Theory, brought on by vigorous processing of the circumstantial evidence and making connections where they seem to make sense as well as a whole lot of guesswork. However it seems quite sound to believe that the little boy from FNAF 4 is what haunts Golden Freddy, given the circumstances of his death. When you think about it, in a very real sense, he too had been 'stuffed' into an animatronic and died because of it… sound familiar?
In the beginning the scandal of an unsolved murder, that is the one of the boy who was seen outside Fredbear's Family Diner that was killed by a mysterious fellow, the diner is eventually forced to close down. Even Fredbear and Bonnie getting a facelift to their modern counterparts and two new characters introduced aren't enough to stave off that fate. It is then bought by the company that would turn it into Freddy Fazbear's Pizza. This company tries to further distance themselves from the accident by taking the current set of characters and making the Toy versions, which are seen in FNAF 2, even going so far as to put the scanning equipment in the Toy models to boast of greater security for kids now. Then the little boy suffered the Bite of '87.
After the accident, the spirit that infested the Puppet helps the little boy gain 'life' and function by binding his soul to the animatronic Fredbear. Maybe the Puppet was lonely and wanted a friend. Maybe he thought it would help things somehow if the little boy could regain something of the life that was stolen from him. Point was, all it did was inspire Golden Freddy to go on a rampage of revenge and murder… by doing to his tormentors in death what they did to him in life. That's right, I'm saying the Golden Fredbear force fed each of the kids into their respective animatronic. Luring them into the back room one or two at a time, and dealing with each of them in turn. Damage incurred during the event, (Bones broken, faces crunched, etc.) causes the death of each kid. Otherwise, it's plausible that the kids would simply be small enough to fit inside the animatronic body without any problems and escape later. The fact that we never see just how the kids were stuffed into the animatronics gives the needed leeway for this theory, especially since none of the kids were discovered until their corpses began rotting. Now stuffed into their robotic tombs, the Puppet, who doesn't quite get what's going on, does for the children what he did for Golden Freddy. Binding their spirits to their animatronic hosts to 'Give them Life'.
This means that the Purple Man, the one blamed and vilified since game 1… was completely innocent. Maybe he stumbled upon one of Gold Freddy's last victims and then was stumbled upon in turn at the scene of the crime. Maybe he simply had no real alibi and was fingered as the culprit since the murders occurred on his watch… for whichever reason, Purple Man goes to jail. Now it's true that the papers in FNAF 1 talked about five kids disappearing instead of just four, but consider this: It's possible that the murder of the mystery kid that became the Puppet and the diner selling off it's name and mascots occurred very close to each other timeline wise. If it had been within a year or two of the four other disappearances, the investigators might've recalled the case and it's similar circumstances. Which in turn would've had them link the two cases together, raising the count of missing persons to the needed five.
The company tries to remove the stain of their reputation as best it can, and Golden Freddy now makes another move to kill again, only to fail. The company completely dismantles the robot out of safety concerns, but soon after the night guards began complaining of the other four animatronics acting strangely at night. This is discounted as fallacy, until the animatronics kill a guard. The company cannot afford another scandal, and so they sweep the event under the rug, so to speak. Soon a new policy is in place. New guards replace those that are either killed by the robots during the night or fired by the company to discredit anything said by them when they went public with their experiences. The policy works, and the urban legend of the pizzeria begins to spread.
After enough time passes, the rumors have spread far and wide, far enough to reach even Purple Man in prison. It is there that he makes the sickening realization: If the animatronics could kill guards… might they have done the same to those kids earlier? Thus he breaks out of jail and journeys to the current Freddy Fazbear's Pizza to destroy the animatronics and stop their rampage. I believe this for a simple reason: If he were the guilty party in the murders, what conceivable purpose could he have in going back there after escaping? There's no point in removing evidence, it had already been used against him. But, if instead, he had come to a realization about the animatronics given the rumors flying about by former night guards he might do so to stop them from killing anyone else.
Which is a true tragedy, since doing so ended the way it did. While he did indeed free the souls of the children sans the Puppet, since his vessel wasn't broken yet, that just meant the angry spirits could now target him directly instead. They frighten him enough to look for any refuge he could find. He spies the Golden Bonnie costume, marred and deteriorated as it is. He remembers that you could put that animatronic on from his days as a guard, as seen in FNAF 4, and does so. The ghosts halt their advance. He sees a way out now, laughing somewhat crazily as he makes a sudden move for the exit…
...the bolts come loose, killing him. Now he, 'stuffed' into an animatronic suit and killed by the experience, is bound to the Springtrap animatronic by the same Puppet that honestly doesn't know any better.
The rest of the story is already known: 30 years pass, the pizzeria chain dissolves. Kids raised on the haunting tales of Freddy Fazbear's Pizza open up Freddy's Fright only to have the place burn down a week into its existence. In theory, the person playing the mini-games frees the disembodied souls of the children (all six children, since the Puppet seems to have been destroyed in the 30 year span of time) allowing them to find peace. But Springtrap was destroyed in the fire, and in theory, that means his spirit is released as well.
One can only hope. And while I shouldn't really steal MatPat's line on the subject...
This too... is just a Theory.