Martin loves to subvert expectations, and this would be a huge way of doing that. That theory has been widely accepted, and now dominates the conversation, but what if it isn't true? George R.R. The most popular theory is R+L=J, which as you probably know by now posits that Jon is actually the son of Rhaegar Targaryen, son of the Mad King, and Ned's sister Lyanna Stark (you can read more about it here and here). The only problem is we don't know what they said.
Martin posed to Dan Weiss and David Benioff, and their answer led to them getting the go-ahead to bring his A Song of Ice and Fire saga to the screen.