Just before Donald J. Trump took the stage at the Republican National Convention in Cleveland on Thursday night, the actor Jon Voight narrated a breezy video biography of the candidate highlighting his can-do abilities.

“He took over another city project tied up in red tape since 1978,” Mr. Voight says with none of the charm or the menace of his character on Showtime’s “Ray Donovan” series. “Donald transformed a landfill into a championship public golf course and saved the city millions.”

But it was a shot into the rough for Mr. Voight and Mr. Trump’s oft-told creation myth of the Trump Golf Links at Ferry Point in the Bronx.

“He did not build the golf course,” said Adrian Benepe, who was New York City’s parks commissioner under Mayor Michael R. Bloomberg. “The city built the golf course. Trump came in as the operator.”