It found Loli had been "unjustifiably" suspended and dismissed as there was not "sufficient information" to support the sex act allegation - the most serious of the two.
However, it did conclude he provided beers to a passenger who was not entitled to them.
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Loli had worked as a flight attendant since 2008, and at the time of the alleged incident was working for VANZ.
During the flight in question, fellow staff members alleged Loli had engaged in a sex act with a passenger in the rear galley.
The allegations were later expanded to include giving the same passenger beer which they did not pay for, to gain favour with them, as well as preventing another flight attendant from coming into the galley to pursue her duties.
Loli was informed of the allegations in June, 2018, which he "strongly denied".
He said he was "shocked and very distressed" upon hearing them.
Loli was subsequently suspended, without being given a chance to respond for two weeks.
The authority found that VANZ did not meet its obligations before suspending Loli, and its actions were "unjustifiable".
"Mr Loli was shocked and then distraught by the suspension," the authority decision said.
"He describes crying and praying, as well as worrying about his reputation, career, community and family."
Further, there were rumours about the allegations circulating at his work, and he was also aware of his situation being discussed more widely.
VANZ carried out further investigations and there were various attempts to meet with Loli and his legal representatives, but after failing to find a suitable time the company terminated his employment on September 19 - by email.
Loli's representative responded that he was "flabbergasted" to have received the email and the company's finding.
He sought a retraction of the decision and for a meeting to be set up for Loli to respond to the allegations.
Loli pointed out inconsistencies between the two flight attendants' various statements, casting doubt on the credibility and reliability of a flight steward and suggesting malice on the part of others interviewed but less central.
In its conclusion, the authority supported Loli's case and found "procedural inadequacies" in VANZ's investigation, and that the allegation of the sexual act was "not substantiated".
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Loli had long wanted to be a flight attendant, and described himself as "heartbroken" when he was dismissed.
The process had a "devastating effect on him personally, socially, professionally and emotionally", and he struggled to find employment afterwards.
The authority ordered VANZ to pay Loli within 28 days $2435 for lost wages during the suspension, $7267 lost wages during the dismissal, and $10,000 as compensation for non-economic loss.