Being sealed away, the Kyuubi had time and motivation to do little things like think. One of the things the Kyuubi constantly thought about and frequently tried was escape. All attempts he had made had failed so far. Attempts at persuaision didn't work. Attempts at sending his Chakra through to control his host's mind didn't work. He didn't give up though. With the mind out, he decided to try the body.
After a great deal of exploration, one of his questing Chakra tendrils found a promising orifice through which it might be possible to exit. Pushing more Chakra in that direction, the Kyuubi was incredibly surprised to find that something was absorbing it at a prodigious rate. The more he pushed through, the more that small something absorbed. Eventually, after he'd depleted nearly a quarter of his Chakra, he ceased his ten-thousandth failed escape attempt.
Neither Kushina nor her husband would have any idea of the consequences of this escape attempt by the Kyuubi for another ten months. Following the discovery of Kushina's pregnancy - which had been a complete surprise to both her and Minato since they'd been taking precautions against children- the medics overseeing her care were constantly frustrated in their attempts at examining the growing fetus due to the interference caused by the Kyuubi's Chakra. Eventually, the pregnancy had run its course, and in due time it was time for Naruto's birth which was to take place in a cave outside of the village due to the possibility of the Kyuubi escaping while Kushina gave birth.
The march through the woods to the cave was relatively silent due to the fact that Kushina's contractions were still several minutes apart and there was a small herd of midwives following her and helping her with the pain as each contraction came. Eventually, the young red-head was led into the birthing chamber which had been specially created for Uzumaki Mito decades earlier after the birth of Hashirama and Mito's firstborn had caused quite the ruckus when the Kyuubi had nearly escaped Mito's seal. Everyone took positions, and the long wait began.
Eventually, the labor during which the Kyuubi's frantic escape attempts intensified as the contractions grew closer and closer came to its final stage and the new baby began to crown, causing Sarutobi Biwako to order Kushina to start pushing. Namikaze Minato held the seal on his wife's abdomen as Kushina pushed. He almost turned to look when he'd heard the startled "Oh Dear!", but knew he couldn't take his focus off of his task for even a second at this critical juncture.
Soon, the Kyuubi was almost entirely pushed back and Minato's newly born and freshly cleaned son was brought into his view as he was laid on Kushina's chest. Upon spotting the child, Minato nearly let the Kyuubi slip from the seal in shock.
"He's...Naruto's..." Minato started, at a loss for words as he looked down at his son, nearly letting the Kyuubi slip through the seal once more due to his distraction. He'd been warned by his predecessor who'd grown up with Hashirama's children that his and Kushina's son would have some Kyuubilike traits, but he'd been led to expect whisker marks on the cheeks, slightly feral behavior, and a propensity for eating raw meat, not...
"Oh!" Kushina exclaimed as she gently ran a finger over one of her newborn son's tiny ears. "He's perfect!"
Perfect wasn't what he would've chosen. He chose not to say anything and completely ruin the moment though.
The moment was ruined an instant later when a masked intruder killed the midwives and snatched Kushina's newborn son however...
Three days after the Kyuubi attack, Sarutobi Hiruzen was left with a problem he didn't know how to deal with. Killing the blanket wrapped bundle that was in his arms would be the logical choice, especially in light of the report that he'd received from the medics who had examined it following the Kyuubi attack, except for one small thing...
Not having another Uzumaki on hand, Minato had sealed the Kyuubi into its son. If the boy were killed, the Kyuubi would eventually reform elsewhere and have a very good reason for actively wanting to completely obliterate Konoha rather than just randomly rampage through the village on its way to gods knew where like it had done after being released from its seal.
People were calling for blood. Blood he could not give them if he wanted to keep the village safe.
Coning to a decision, the newly reinstated Sandaime decided to do the only thing he could think to do in this situation. That was to turn things back on the village rather than the Kyuubi's jailor which must be kept alive at all costs despite what people might personally think about it. A jailor that unfortunately the whole village knew about rather than the few who needed to know, and the few who had found out later. Despite Kumo's having kidnapped Kushina over the fact that she was a Jinchurriki, few people really knew that Kushina had been the host of the Nine-tails. That wasn't the case now.
Few people had really known for a fact where the Kyuubi had been since the Valley of the End, though many had had their suspicions. Others who had known about Mito hadn't known or hadn't known for certain that Kushina had been the Kyuubi's jailor. Then, there was the fact that the Kyuubi which had somehow managed to impregnate Kushina had not shown an obvious gender...
Using these facts and his knowledge of the unknowing ignorance of the average Konoha citizen, Hiruzen began to map out a new reality for the boy and the village.
Crafting a fairytale of an angry mother animal that had been riled up by a person or persons unknown, and a Yondaime who had found a baby animal in a cave and begged for mercy on it before he died after sealing mother inside of child, the unretired Hokage stroked the small, red-furred, nine-tailed baby fox that now rested on a blanket in his lap with the hand that wasn't writing the tale that would probably have Danzo wondering if he'd completely lost touch with reality. When the last words of the sentimental mush that was meant to pull at the heartstrings of the civilians and quite a few of the shinobi who still had feelings were written down, the Hokage put down the claim that the small animal who would likely be able to speak one day was named Uzumaki after the family of Uzumaki Mito who had sealed the Kyuubi in an "undisclosed location" from which it had been inadvertently been released after the Valley of the End, and Naruto since it had been the name the Yondaime had picked for the creature he had carried out of the cave on the night of his death. Both reasons for Uzumaki Naruto's naming were technically true, but not in the way he was intimating.
Two days after the Hokage's missive detailing how someone had allegedly messed with the Kyuubi which had just been trying to protect its kid went out, Uchiha Fugaku stood and stared down the four members of his clan who had been summoned to his office.
"Explain yourselves." he said to the four young men who were nervously shifting in place, intimidated by his cold, silent glare.
"Explain what Fugaku-sama?" one of the men who was only just out of his teens asked.
"Several villagers claim to have seen you four entering the forest on the night of the Kyuubi attack with a case of beer in your possession." Fugaku snapped.
"We never went anywhere near the Kyuubi!" one of the men who was technically a teen exclaimed, realizing what he'd been accused of.
"Damn, we didn't know the Kyuubi was even in those woods until we woke up the next morning and found out there was an attack!" one of the others said.
Edited 1/2/16.