It follows comments yesterday from Health Minister Chris Hipkins not to believe everything on social media.
He said the daily 1pm press conference was designed to give people the most complete picture as possible.
Talking about misinformation and speculation rife on social media, he said there would be much more public concern if test results were published in real time.
"My advice to everyone is, if you hear it here at 1pm, it's true."
A spokesman for the Government's managed isolation and quarantine team told the Herald they were aware of the rumour claims, and they had been investigated by the managed isolation facility manager and by the onsite security manager.
"There were no reported incidents and there is no evidence of such a breach occurring at the Grand Millennium during the time period mentioned," he said.
"There has been no link established between the community outbreak and a facility at this point."
As Auckland entered its fourth day at level 3 - and the rest of the country level 2 - there were seven new cases of Covid-19, director general of health Ashley Bloomfield revealed.
All were in the community, with no cases in managed isolation. Six cases were linked to the Auckland cluster and one case was being investigated.
That was in addition to the case being investigated yesterday. Bloomfield was confident both cases were linked to the cluster.
There are 56 active cases in New Zealand, of which 37 are in the community.