Mr Miller told the authority he had made the comment "in jest".
But when contacted today, he denied saying it.
"I've made comments, but I've never said what Mr Searle is saying I said."
Mr Miller described what he did say as "regular work banter".
"It's a construction site. Have you ever been on a construction site and listened to the banter between some of the guys?"
He said Mr Burrell was a good friend and they had had a beer together at his house that night.
"If Mr Burrell had a problem with anything I'd said, he would have brought it up with me. We never had any such discussions that I'd ever overstepped the mark on something that he thought was offensive."
The authority's determination, released today, said there was obvious conflict in the evidence about the effect the comment had on Mr Burrell.
It noted written evidence that Mr Burrell was "clearly still upset" about the comment more than a year later.
But Mr Burrell, who has since moved to Australia, gave written evidence that he and Mr Miller were joking when the comment was made.
"I didn't take offence and laughed it off."
Mr Searle claimed Mr Burrell had been paid $1000 to sign the written statement before moving to Australia.
Authority member Kenneth Anderson accepted Mr Searle's evidence that the comment was inappropriate and said he was entitled to treat it as serious misconduct.
But he found Mr Searle failed to observe basic minimum requirements of proper dismissal procedure.
Mr Searle had failed to notify Mr Miller of the allegation against him, did not give him a chance to refute the allegation, and did not give unbiased consideration to the matter.
The authority found Mr Searle should pay Mr Miller for the three weeks of income he lost before he was offered another job, but halved the amount owed to $960 due to Mr Miller's culpability.
It dismissed Mr Miller's claim for compensation for hurt and humiliation.
Mr Miller told APNZ that although the authority found in his favour, he felt like he had lost the case.
"I'm furious, I think it's highly unfair," he said.
"I'm happy that I've won, but I feel like the law, and by association the whole system, has treated me unfairly. Because I wasn't the one put on trial - he was put on trial. He was supposed to follow the letter of the law to dismiss me."
Mr Miller said his former boss had made the allegation because he had "a vendetta against me".
Mr Searle said he had found Mr Miller's comments "absolutely appalling".
"No one on any worksite should say that to a fellow employee and that's what I took deep offence to," he told APNZ.
"The guy was in tears."
He still felt aggrieved by Mr Miller and said the issue should never have gone to the authority.
Both men said they were thousands of dollars out of pocket after the hearing.
