WOW... Now my minds blown, but it makes sense
Yeah. If it's true, that would make him the rightful heir to the throne (which I could see). People believe that's why Eddard Stark never actually calls Jon Snow his son, but instead, calls him his blood. He addresses his other children as his children. I think in the books, Lyanna Stark is abducted by Rhaegar Targaryan (the prince at the time), and was supposedly raped and held in the tower of joy. Robert Baratheron (King Robert in the show) started the rebellion to get her back, and after Aeris Targaryan II is killed by Jaime Lanniser, and Ned arrives and so on, Robert sends the armies to kill all of the Targaryan children and other family members. The tower of joy was the last place they checked, and they found 3 of the king's guards there, battle ensued, only Ned Stark and Howland Reed (a bannerman) remained alive. Ned reaches Lyanna, finds her dying (bleeding out, from what is unknown, but it's possibly child birth) and her last words to Ned Stark are "Promise me, Ned.", to which he promised to fulfill. What he promised to her is unknown, but many believe that the promise is that he will take an infant Jon Snow home with him, claim him, and raise him as his own so Robert does not have the baby killed (because he would be a Targaryan baby).
Other things that might support that is just how honorable Ned was (to the point that it got him killed). A lot of people find it hard to believe that Ned would actually cheat on his wife. That's essentially what it is.