The five wrote a letter to athletic department officials after they said Fisher failed to understand their concerns, aired during a meeting with the players, The Salt Lake Tribune reported Thursday.
In the letter, the golfers accused Fisher of endangering them and not realizing 'the gravity of his actions or the importance of his responsibility as a coach, guardian and role model.'
Fisher said he has not read the letter.
'In my mind, there's nothing to substantiate' the golfers' concerns, he said.
Utah assistant athletic director Marc Amicone met last week with the players and then with Fisher.
'The only thing I can say is we investigate any comments about a coach and deal with them, and that's what we've done,' Amicone told The Tribune. He did not immediately return a message left at his office Thursday by The Associated Press.
The alleged incident occurred April 27 as the team flew to Portland, Ore., and then drove to the Mountain West Tournament in Sunriver, Ore., about four hours away by vehicle.
When their flight arrived, the golfers 'all felt [Fisher] had too much to drink and were very hesitant to step into a vehicle with him behind the wheel,' according to the letter.
'I knew that he shouldn't be driving,' Luke Swilor told the Tribune. Added teammate Casey Fowles: 'We sat on the edge of our seats for four hours.'
The golfers discussed the ride during their practice round the next day and, after talking in their hotel for nearly three hours, according to Fowles, asked Fisher to join them.
They said they were disappointed with his lack of contrition, which led to their meeting with Amicone the following week.
The subsequent discussions 'caught me off guard,' Fisher said. 'I thought it was all done. ... There was certainly nothing I expected there to be a concern about.'
Fisher told the golfers he had only two drinks and 'would never put you in harm's way,' according to the letter.
Fisher, 45, said he will sign a statement that any behavior resembling what the golfers alleged would be grounds for termination in the future, while strongly disputing their account of his condition.
'I in no way felt I jeopardized anything' regarding the golfers' safety, Fisher said. 'It's their opinion.'
Fisher, a former Ute golfer and an award-winning teaching pro employed by The Country Club of Salt Lake City, is completing his ninth year as Utah's head coach.
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