An Auckland GP is now calling for all New Zealanders who have symptoms to be eligible for a test.
Newshub has learned of multiple cases of people getting referrals from doctors for a swab only to then be denied the crucial check at dedicated COVID-19 sites.
Marist College in Auckland is a "coronavirus cluster" site after 10 staff and 6 students have tested positive.
Other parents from the school think they or their children might have it - but are being blocked from finding out.
A Marist College mother, who's got a fever, says she was told by Healthline that neither she nor her daughter, who also had symptoms, qualified.
And that uncertainty only puts others at risk.
"I'm really worried there could be an explosion of cases in the Marist communities," she told Newshub.
She eventually got a test, but only after she demanded one at a drive-through testing station.
The school board’s chairperson says the community is worried.
"They're scared and afraid," Stephen Dallow told Newshub.
Which is why the school wants the Ministry to act.
"It would be such a reassurance for our families for anyone connected to Marist to be tested."
The Government's criteria allows doctors to refer patients for swabs, but even with a health professional's referral, people are still being rejected.
Newshub has spoken to an Auckland man who says his wife, who has symptoms and possible contact with a COVID-19 case, was referred twice by two different GPs to get a swab for the virus. However, after waiting hours at two different testing stations, she was told she did not qualify.
The Ministry says it's determined to hunt down cases but Dr Garsing Wong says people are being turned away even with a clinicians referral.
"Unfortunately that isn't acceptable. We really need to open it up so that any symptomatic patient can be tested," Dr Wong told Newshub.
He says until that happens, we won't know the full scale of the crisis.
"At the moment with our testing regime, we are underestimating the prevalence or the amount of infection we have in our community,"
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He's even had a colleague's cancer patient being denied a test - and the patient's operation had to be cancelled.
"[It's] totally inadequate that a delay in a surgery could happen because we can't do testing."
The UK's getting millions of at-home finger-prick test kits, which can tell if you've had the virus and are therefore immune.
Immunologist Dr Nikki Moreland believes they could be a crucial part of the fight - particularly for keeping healthcare workers safe.
"What these tests have the potential to do is to look at whether someone has antibodies in their blood to the COVID-19 virus,"
The ministry says it currently has no plans to implement home testing, but that could change.