In a Facebook post, the pharmacist alleged Gayford had said the Ministry of Health policy had changed and allowed close contacts to get an RAT.
Gayford admitted a friend had put him on speakerphone while in a pharmacy to discuss RATs, but did not give his version of the phone call. He apologised for any "confusion".
On Thursday, the Prime Minister's office refused to answer further questions about the extent to which this was a one-off occurrence, and whether it was appropriate for him to try to get the test.
When other media approached the Prime Minister's office about the story, the office refused to comment, but referred reporters to a statement issued by Gayford's managers.
But on Thursday morning, Gayford's managers were not issuing his statement - already published by the Herald - to other media, impeding their ability to cover the story.
In a news story, TVNZ's 1News said it "approached Gayford's management team for a response," after being directed there by the Prime Minister's office. However, Gayford's management "refused to comment".
Only in the afternoon were other media able to obtain the statement - after some had raised the issue with the Prime Minister's office. Gayford's management blamed the delay on holidays and staff needing to talk to senior management before sending the statement.
Gayford's management refused to answer further questions about the incident.
When asked whether Gayford had made similar calls on any other occasion, his management said they would not be commenting further.
National's Covid-19 spokesman Chris Bishop said the behaviour showed a lack of transparency.
"This behaviour is not consistent with the idea that this would be the most transparent government in New Zealand history," he said.
"The Prime Minister might not want to answer questions about this [but] that does not mean it's acceptable behaviour," he said.
Act leader David Seymour said he did not usually bring politicians' partners into politics, but he commended Gayford for trying to get RATs, as widespread RAT use is Act policy.