Yeah man this whole idea is WAY off.
Not only did Cersei not have a child that died in the books, but the line from Ned to Jon about having his blood isn't even in the books. That whole interaction was completely new from the series. I actually think it was a great addition though. Ned and Jon never even have a farewell scene in the book.
It's similar to the scene with Tywin and Jamie in the tent when Tywin is skinning that deer. It's a great scene that gives a lot of background on the relationship, but it was not in the book. Still a good device by the producers.
I'll say this though for Kash, I read the books AFTER watching season 1 and I thought the same thing he did. I was convinced Jon was Robert's heir just didn't really know how yet.
Then I read the books
It could just be the show's way of introducing some doubt for the viewers about Jon being Ned's son since the LS/RT storyline is given virtually no time without the flashbacks and references to the TOJ.
Still my biggest complaint with the series.
This post was edited on 3/3 at 1:54 pm