Reminder that Stannis based his claim on the throne on nothing more than a court gossip and a book that only states the colour of the hair his ancestors. There were no knowledges of genetics in Westeros at the time, and nobody ever watched Cersei and Jaime having sex nine months before her children were born. The only evidence that could prove that Joffrey, Mycella and Tommen weren't Robert's children was Cersei's word to Ned, although it was very likely that she lied to him so Ned would start an impulsive rebellion, and she would have a reason to get rid of him.