What if the telephone game screwed up the Night's King story and Bran didn't bother fixing it?

Potential Spoilers Below

If you have read my theories, I believe that most of the stories of old come from what Bran knows of the present and when he goes back in time, he passes those stories along. 

Time travel hurts my head

Bran can only see the past; he can’t see the future

“The gathering gloom put Bran in mind of another of Old Nan’s stories, the tale of Night’s King. He had been the thirteenth man to lead the Night’s Watch, she said; a warrior who knew no fear. “And that was the fault in him,” she would add, “for all men must know fear.” A woman was his downfall; a woman glimpsed from atop the Wall, with skin as white as the moon and eyes like blue stars. Fearing nothing, he chased her and caught her and loved her, though her skin was cold as ice, and when he gave his seed to her he gave his soul as well.”

“He brought her back to the Nightfort and proclaimed her a queen and himself her king, and with strange sorceries he bound his Sworn Brothers to his will. For thirteen years they had ruled, Night’s King and his corpse queen, till finally the Stark of Winterfell and Joramun of the wildlings had joined to free the Watch from bondage. After his fall, when it was found he had been sacrificing to the Others, all records of Night’s King had been destroyed, his very name forbidden.

But what if the story got passed along in the wrong way.  What if the person who is to become the Night’s Queen, Daenerys, glimpsed a man, Jon Snow, who had been a man who had led the Night’s Watch from atop the Wall?  His skin was as white as the moon because of his exposure to the elements; he himself looking like a corpse with all his wounds.  Maybe when he gave her his seed, she gained possession of his soul because she becomes pregnant with their child and she somehow use the child against him when she goes "dark"; as I believe she will.

Why I believe Daenerys is “Breaking Bad.”

The "Truth" of who she really is.

Dany glimpsing Jon from atop the Wall

Instead of the Nightfort she took him to her ship

Jon's corpse like body

He gives her his seed

Comments encouraged.  Love to hear the idea’s of others.  Most believe that since I present my idea’s as “fact like” I’m not open to change my viewpoints which is far from the truth.  I simply look at the information presented and go from there.  If you can shine a light on another way of thinking that opens the door to debate.