Mark David Chapman (related to Bill?) never denied doing it.
Quote from Wikipedia:
“As Lennon walked into the building's archway with his wife Yoko Ono, Chapman fired five shots at Lennon from several meters away with a .38 Special revolver. ... Chapman remained at the scene reading J. D. Salinger's novel The Catcher in the Rye until he was arrested by police.”
Good point. However, if MDC had had an opportunity (like the one that apparently fell into LHO’s lap) to conceal himself and fire a rifle from a distance, would he have been more likely to try an escape and, if the escape was successful, then deny it if caught later?
LHO was escaping from his aunt’s house at night when others were asleep when he was very young. His flight after the JFK assassination was a challenge to his Houdini skills.