Air NZ does not sponsor the NZOC but deals directly with athletes instead.
The Weekend Herald has been told the standoff was serious, and that the NZOC told Air NZ it was putting the athletes in breach of the rules.
The NZOC told the Weekend Herald it was trying to make sure athletes were not affected, but did not explain how the situation was resolved with Air NZ. It appeared a waiver was eventually granted as the campaign continues to run.
"We took all possible steps to ensure the athletes were not ... affected in any way by any commercial discussions and we ensured all appropriate waivers were granted," said NZOC spokeswoman Ashley Abbott.
"Our primary objective was to protect the athletes from being involved in any actual or potential breach and ensure their focus was able to remain on the Olympic Games."
Abbott said the NZOC has a "strong commercial relationship with Air NZ", which had flown many athletes and officials to Rio.
Air NZ said it would respond to questions, but had not by deadline.
For athletics star Adams, it's the second time her Olympic preparation has had to react to serious, last-minute administrative issues. An astonishing blunder in London four years ago saw New Zealand officials fail to register Adams for her defence of the shot put Olympic gold.
Luckily, an Australian official came to the rescue and helped persuade the IOC to let her in after the registration deadline.
Last night Adams' manager, Nick Cowan, said he believed Air NZ's campaign had not breached Rule 40 stipulations - a measure he said added "a new layer of bureaucratic process".
"Rule 40 and its implementation in New Zealand had not provided the flexibility that was perhaps intended," Cowan said.
"The rule adds a new layer of bureaucratic process that made things time-consuming and challenging for the athletes and their commercial interests."
Cowan said he wants the application of the rule to be addressed.
"I hope that after the Games we can find a way for [application of Rule 40] to work as intended so athletes and their national sport organisations can leverage partners in a fair and equitable manner."