Question:

      Why do stars claim they do the stunts performed by their stunt doubles?

Answer:

It is often part of the publicity script.

    Stars do not tell tall tales of daredevil stunts on television out of either personal dishonesty, vanity, or egoism. It is their job to play a character in publicity appearances, just as it is the job of studios to hype their movies. Nor do others in these Hollywood productions– even if they were not bound by contractual restrictions on disclosures, or "NDAs"– have reason to demystify such off-screen fictionalizing. The subterfuge is part of the system by which studios, talent agencies, music publishers, licensees, and others create, maintain, and profitably exploit the stars’ public personalities.  Stars therefore assume they have license on talk shows to fantasize about performing perilous stunts that stunt people performed.