Nobody knew that the records of the years after the founding of Hogwarts were written by a murderer who was covering up her crime. Salazar Slytherin had never left Hogwarts, in fact his bones are still somewhere in the castle.
The arguement with Gryffindor did take place, however it wasn't the cause of Slytherin's leaving (after all, he never left), nor was it about what history says it was about. Purity of blood wasn't really an issue for him, he just felt that muggleborns would be more apt to make some sort of mistake that would end up with the school being destroyed by the church, and therefore were less trustworthy. It had happened to the wizarding school in Rome a century before. An ancient wizarding school lost just because some muggleborn had decided that he felt guilty and had to confess that he was a wizard.
The chamber of secrets was actually the lower catacombs of the school, Slytherin thought it would be funny to have a giant statue of himself down there since putting it elsewhere in the school would look rather tacky. Down in the catacombs beneath the school however, it looked imposing, especially with the snake statues surrounding it.
I digress. To know the true history of the founders you must come with me to see Salazar's "Deathbed Confession". Wizarding confessions are not like those of muggles, at the moment before their death a wizard who has been trained in this process will place all of their most important memories in some sort of medium. For us to see his, we must look into this pensive that is in this room full of rotting furniture, next to this bed with a skeleton with a dagger in it's chest on it.
We shall skip past the childhood memories, including the interesting one where he fell off a cliff and landed in a nest of adders, this apparently is how he discovered that he was a parcelmouth. And the one where he got bit in the ass by the neighbor's hunting hound. We'll stop and look at the one where he met Gryffindor. Ouch, that's gotta hurt, never mind, we'll skip it. Ooh here's where he met Ravenclaw, look he's getting the crap knocked out of him. Here's where he met Hufflepuff, isn't that cute, she's rescuing him from her Venomous Tentacula.
Ahem, we'll just ignore this one and skip to the founding, I don't think you'd want anyone watching you on your wedding night. So what if it's hilarious that he has no idea what to do, he'd figured it out eventually, after all he does have descendants.
Oh look they're building the castle, there's Slytherin over there running from the bowtruckle screaming like a girl. Must be some ploy to make people think he's stupid and helpless. No? You mean that one of the greatest wizards of all time is deathly afraid of bowtruckles?
Look they've got the castle built, now they're rounding up students. Looks like Slytherin stole half of his from Durmstrang. The headmaster of Durmstrang looks really pissed, I don't know if it's over the stolen students of if it's because Slytherin is giving him the one fingered salute, either way he's pissed.
Now they're getting on in years, back then sixty was old for a wizard. They're making the sorting hat. Neat, it's insulting Gryffindor, something about his head being almost entirely empty, and being extremely lucky to have lived past the age of two. It's not an insult? You mean the hat was stating facts?
Here's Salazar's last day in the castle, according to the official history of Hogwarts, Salazar is going to get into an arguement with Gryffindor over accepting muggleborn students, build the chamber of secrets in hopes of ridding the school of non purebloods and leave. Several things are wrong with this however, if you were paying attention earlier, you'd have noticed that the so called "Chamber of Secrets" has already been built. And two, at least half of Salazar's students are what will later be called mudbloods. We shall now see what the arguement was truely about. Listen carefully.
Gryffindor: Look, having that creature in the catacombs to protect the school from an underground attack is okay, but I don't want it slithering about the halls at night.
Slytherin: Look, if people knew that there was a basilisk roaming the halls of the school at night, they'd be less apt to invade, and the students wouldn't dare set foot outside their dormitories after hours. It's the perfect solution.
Gryffindor: How will we be able to control it once you're gone? What if it kills one of the students? What if it eats someone?
Slytherin: At least one of my descendants will be at the school at all times, they'll control it. It won't kill any of the students if they stay in bed when they're supposed to. Hopefully, the only person it'll eat will be an intruder foolish enough to tresspass in the castle.
Gryffindor:Your arguement is convincing Salazar, but that creature stays in the catacombs and protects the underside of the school, that's it. If I see a single green scale, I'm going to kill it myself.
Slytherin:You wouldn't, Minky's just a baby.
Gryffindor:Minky is a dangerous creature, and if I see her anywhere in the castle I will, and that's final.
Slytherin: You bastard. Don't talk to me, I'm going to my room.
By the next morning Salazar's known belongings and his grandson were gone. We shall now see what happened that night.
Salazar Slytherin awoke with a start, someone was in his private inner sanctum. Only two people knew about his other set of quarters, himself and Roweena Ravenclaw. He looked over, it was her.
"I don't want to talk to anyone right now. I'll be done sulking in the morning, you can come back then."
"You can't have him."
"What? I don't know what the hell you're talking about, be more specific."
"YOU CAN'T HAVE HIM! HE'S MINE."
"Who's yours?"
"Edmund."
"Edmund? Edmund? Oh yes him, the hat gave him to me when we decided to test it out this year. I guess that makes him mine."
"He's mine."
"Look, let's quit arguing over who some lousy student belongs to right now. We can discuss this at a more civilised hour, right now I want to get some sleep."
"Okay, we'll discuss this in the morning."
"Good. Oh, and by the way, the hat gave him to me, he's mine."
"AAAAAARRRRRRRRRRGGGGGGGGGHHHHHHHH!"
"I'm sorry it had to come to this Salazar. He's mine, his father was mine, his grandfather was mine, he's mine. If killing you was the only way to get him back then so be it."
Now my friends, with the last memory in the pensive we all see the truth. Lady Ravenclaw murdered Slythein while he was in his bed in an arguement over a student. Thanks to her lies, Slytherin and Gryffindor students have been at each other's throats for centuries. Now you see the pointlessness of it all. All for the sake of a student the unity of a school collapsed.
1000 years ago, shortly after the death of Salazar Slytherin:
There was still blood on Lady Ravenclaw's hands when she rescued her youngest grandson from the clutches of the students of the most despicable man she knew. The man she had loved, but who had turned her down so long ago.
She now had to cover up her crime. She knew exactly what to do.
The letter to Anzarr Slytherin arrived shortly before dawn. He obeyed immediately, there was no contradicting his grandfather.
While Anzarr was packing, Lady Ravenclaw was instructing the sorting hat to not place any muggleborns in Slytherin, half bloods were okay.
When Gryffindor asked where his friend went, she told him that he left for good after their last arguement. Gryffindor mourned the loss of his friend, and hoped that he'd return, he knew better than to go after him.
Anzarr Slytherin waited a year and a day for his grandfather, when it was clear that he wouldn't show, he threw the letter into the fire and watched as the handwriting changed. He'd then realized that he'd been tricked. Upon returning to Hogwarts, he'd discovered that the wards had been adjusted so that neither he nor the next seven generations of his family could enter.
The final piece of the cover up took place after Goderic Gryffindor and Helga Hufflepuff died. Shortly after their deaths, Lady Ravenclaw burned most of their papers and wrote her own version of Hogwart's history, putting Salazar in a very bad light. After a couple of generations, the truth was lost and even Slytherin's own descendants came to believe her tale.
For a thousand years the bones of Salazar Slytherin lay undisturbed in a set of quarters that nobody knew existed. Until now, nobody knew the real story of a founder named Slytherin, now my dear you know. Tell the others, let them see the lie that will destroy us if we let it. Gryffindor and Slytherin need to stand together like they did long ago if the school is to survive this war.