Perhaps you have evidence to the contrary?
Allow me this imperfect analogy. In a discussion by parent and adult child, child asks parent if they know a certain relative. Parent knows relative and states the wife had a miscarriage. No medical record of the miscarriage was made.
Since this was an important piece of family history, the story was told and retold through the generations.
Several generations later, in writing a family history, a “modern” relative recounts the story, but admits no records exist.
In light of this circumstance, would you call the story fiction?
Peter was not a pope.
In matters of nobility, royalty, and succession: In a word, YES. Claims to succession require proof as a matter of course, else it is not succession. Papers, please.