She gave good reason for her beliefs, but Shari Beck gave good reasons for believing she WAS diane's daughter. Diane Haegar, who wrote, Courtesan, also thinks it's true.
My main reason for believing this stem from Diane's reaction to Janet Fleming's pregnancy. She flew into a rage, and understandably so. She refused to see the child, let alone raise him with other's other children. Contrast this to her "reaction" to Diane de France.