(By the way, during Season 1 through, say, 5, did we have an idea who Jon Stark's mom is? We "know" he's Ned's bastard, but what was the story that was told? He - obviously - wasn't Catelyn's, but what was the understanding BEFORE Bran's flashbacks to the tower and Lyanna came up in Season 6?)
This wasn't changed for the TV show, so it was in the books as well and all you had to do was going online to find the theory discussed. So everyone who bothered to write on Google "Jon's true parents" would have long known what was the leading theory for ages.
It was so discussed that the actual surprise would have been Jon NOT being the son of who eventually turned out to be the parents.
But that wasn't my question. I wasn't asking what the theory is/was, I was asking what did we KNOW. What did Ned tell Jon about his mother. I think the answer is "not much", so the premise I'm working on is that as of Season 6 Episode 10, JON SNOW believes his dad to be Ned Stark and he doesn't have even a hint as to who his mother might be.
But Bran has information - and we have slightly less information, assuming Bran knows what the whisper is and we don't - that Jon doesn't, that Ned's sister Lyanna gave birth to a baby that we're heavily influenced to believe is Jon Snow (the full screen shot of the baby, then the full screen shot of Jon Snow is about as subtle as GG Allin), which means that unless Ned engaged in some pretty heavy duty Lannister shit, Ned's not the father after all, and Jon is not of House Stark. (Which also has repurcussions, potentially, since that means that Sansa is the next in line to be Queen Of The North, which of course might change Peter Baelish's thinking.)