Finlayson's daughter Nicole watched Tuesday's press conference and said she was initially elated after hearing her mother was "stable" instead of "critical".
"I rang my dad to see if he had received a further update from the hospital, he hadn't. I rang the hospital and they confirmed she was still critical. This was a little heartbreaking," Nicole told RNZ.
Director general of health Ashley Bloomfield yesterday gave the family a sincere apology for any upset caused and said by "stable" he meant there'd been no change in her condition.
"But I am very sorry because I think ... that did create some anxiety and concern for the family.
"So I am sorry that happened and I am certainly happy to be in touch with them personally if they would like to."
Ardern said officials were looking at changing the language used to describe people's conditions.
"No one wants to create any kind of extra additional distress for families, as has obviously been caused in this case."
Yesterday's daily tally of three cases was one of the lowest since the first Covid-19 case was confirmed in New Zealand on February 28.
But the total number of cases - 1451 - remained the same, as three infections from Wednesday have now been included in Uruguay's statistics as they'd been tested there.
The number of people who've recovered was 1065, meaning there were fewer than 400 active cases.
There were 6480 tests on Wednesday, bringing the total tests processed to more than 101,200.
And as New Zealand draws closer to the end of lockdown at 11.59pm on Monday, Coster said most Kiwis had responded well to it.
But there had been 4452 breaches - 423 in the past 24 hours - and 477 prosecutions, 3844 warnings issued and 131 youth referrals made.
Coster reminded Kiwis they were still under lockdown this Anzac weekend, and warned there'd be checkpoints for anyone with fixings of going to the beach.
Under alert level 3, there would be looser restrictions on movement but it would be a high trust model, Coster said. But police would act on clear breaches, like public gatherings.
There was also more information about health services available under alert level 3.
Dentists would be able to provide "urgent face-to-face appointments" under alert level 3 but not routine dental care.
Bloomfield said community midwives could continue "the fantastic work they do with pregnant women out in the community, using virtual means where possible but also face-to-face".
There would be some allowances for face-to-face physiotherapy, podiatry and optometry, where urgent care is required. But they would continue to provide services virtually.
Community mental health care would be done by virtual means or phone but face-to-face appointments could be done "if necessary".
And family visits to aged residential care facilities for palliative and compassionate reasons would be considered on a case-by-case basis, Bloomfield said.
Hospitals, GPs and community pharmacists would remain open like they were during the lockdown.
Hunting will also be permitted under alert level 3, as Ardern said it was an important part of providing food for families in parts of the country.
But there were restrictions - hunting was only allowed if done safely, on private land, within your region and bubble and done on foot.
Duck hunting season has been pushed out for a couple of weeks.
Embattled media companies were also thrown a short lifeline with a $50 million support package which included cutting transmission fees for broadcasters for the next six months and Government departments bringing forward advertising spend.
There was also an $11 million fund established for "specific targeted assistance to companies as and when needed".
The announcement followed concerns that the border exemptions for air crew were a weakness that could open the door to an imported case of the deadly virus.