This complaint was then referred to the Broadcasting Standards Authority (BSA).
In its decision, released today, the BSA said it believed TRN took sufficient action.
"The Radio Network has apologised to the complainant for the offence caused.
"The host issued a lengthy apology on air the day after she made the comments, and we think she was sincere in that apology. The broadcaster also issued a public apology," the decision said.
The BSA said it understood some listeners found the comments objectionable, but did not think they reached the high threshold needed to find a breach.
"This was not a calculated or deliberate attack; these comments were off the cuff and never intended to go to air."
The BSA also declined to uphold complaints that comments about climate change made by broadcaster Mike Hosking were inaccurate and misleading.
On TV One's Seven Sharp programme earlier this year, Hosking said that, according to a 2600-page Intergovernmental Panel on Climate Change report, "we are going to climate hell in a handcart".
"That's of course if you believe them which it turns out I don't."
He also questioned predicting the climate in 86 years' time "if the MetService struggles with the accuracy of a five-day forecast".
Four viewers complained to the BSA that Hosking's comments were misleading and inaccurate.
In its decision, the BSA said Hosking's comments were clearly his personal opinion, as opposed to statements of fact, so were not subject to standards of accuracy.
The authority said that in its view, the complainants read too much into Hosking's comments.
"Viewers would have realised that this monologue was an expression of his opinion, and would not have taken the comments as an authoritative conclusion on the topic," the decision said.