However, an unearthed interview with George R.R. Martin seems to disprove the notion that the Targaryens were supposed to be immune to fire.
According to Reddit, in an interview from 1999, George spoke to a fan site about the books, and in particular, the scene in which she came out of the fire with her newly born dragons.
During the interview, he responded to a question regarding Daenerys, saying: “Granny, thanks for asking that. It gives me a chance to clear up a common misconception.
“TARGARYENS ARE NOT IMMUNE TO FIRE! The birth of Dany’s dragons was unique, magical, wondrous, a miracle.