In the movie, Sonny Liston moved to Las Vegas in 1962. Liston moved to Denver from Philadelphia, not to Las Vegas. He didn't move to Las Vegas until after the second fight with Muhammad Ali.
Sonny Liston's disappointment from a lack of fan and media attention, after he won the title, didn't happen outside his dressing room...it happened after he returned home, when he landed at the airport in Philadelphia.