Cheika and Peyper had a discussion at half-time during the Waratahs' clash with the Auckland Blues on March 28, prompting a complaint from the New Zealand side.
Coaches are prohibited from having any discussions with match officials during the course of a game and SANZAR duly reprimanded the pair after conducting an investigation.
With Cheika already under a suspended six-month ban for a hot-tempered exchange with a camera-man in South Africa, New Zealand media slammed the verdict and criticised SANZAR for going soft on "cheating".
"Certainly the word cheating has not entered into any of our thinking at all and it is a pretty strong accusation," Peters said in comments published by Fairfax Media.
"If there was any evidence of cheating we would certainly have taken a different course of action, but we absolutely refute that there was any evidence available of that action or intent.
"We stand by the evidence provided by both Jaco Peyper and Michael Cheika about the nature, tone and timing of the exchange."
In its initial finding, SANZAR said it was satisfied the exchange between Cheika and Peyper was just to clarify an interpretation of refereeing the scrums.
SANZAR did not regard the episode as a code of conduct violation, which would have seen Cheika automatically banned from the game.
"In this instance our job was to only look at the incident we have in front of us, and to ascertain whether it amounted to misconduct," Peters added.
"In this set of circumstances we don't believe it was."
Cheika defended his part in the exchange over the weekend, remarking that he was "obviously ... not liked over there or not respected" in New Zealand.