As the story goes, back in the Age of Heroes, not long after the Wall was raised by Bran the Builder, a certain brother of the Watch rose to become the order’s 13th Lord Commander. He might have been a Stark or a Bolton or even a Skagosi from the cannibal island of Skagos. In those days, the Watch was headquartered at the Nightfort, the largest of the Watch’s strongholds, and the castles along the Wall were fully manned. The tales agree that one day, while standing guard atop the Wall, the Lord Commander glimpsed a woman—with skin “white as the moon” and eyes a ghostly blue—in the woods on the northern side. Was she a sorceress? Some kind of White Walker? Or, like Benjen Stark, something in between? We don’t know. But the Lord Commander was enchanted … and apparently aroused. He left his post, crossed to the far side of the Wall, found her, and made love to her.
The Lord Commander returned to the Nightfort with his pale bride. He declared himself the Night’s King and the pale woman his queen. His former Night’s Watch brothers fell under their dark spell. Soon the Night’s King and his white queen had carved out an evil kingdom for themselves there in the shadow of the Wall with the Nightfort as its foul capital. For 13 years they reigned.
It took an alliance between Brandon “The Breaker” Stark the King in the North and Joramun the (first?) wildling King-Beyond-the-Wall to bring down the Night’s King and his queen. In the aftermath, when it was discovered that the Night’s King had been making sacrifices to the White Walkers, all of the Watch’s records pertaining to his time as the 13th Lord Commander were purged and, in a Voldemortian move, even the mention of his name was forbidden. This, in my opinion, lends credence to the idea that the Night’s King, at least in the books, was a Stark. House Stark and House Bolton, even then, shared a long and bloody history of mutual enmity. If the Night’s King was a Bolton, publicizing that fact would be useful to the Stark kings in the North. If he was a Stark … well, that would need to be covered up. Who else would have the power and influence to do that but the Starks of Winterfell?