Abercrombie's wife Monique-Raquel and his three children were granted an exemption to complete their 14 days mandatory quarantine in their home after travelling back from Australia.
Monique-Raquel tagged Prime Minister Jacinda Ardern on social media, complaining about the state of the hotel room they were placed in, which is believed to have been in a facility near Auckland International Airport.
Abercrombie, who is in Australia with the rest of the Breakers team, told Newstalk ZB's Heather du Plessis-Allan two of their three children have high needs, prompting them to file a medical exemption.
"[They] have significant behavioural and medical issues, I don't want to go into the details of what those are," he said.
"The evidence that we put forward in our application was enough for those powers that be to decide that was the best thing for them, so they're obviously significant enough for those people to make that decision.
"The fact that I am a basketball player or where I live had absolutely nothing to do with that decision and I'd be very disappointed if it was.
"I'm extremely disappointed and frustrated."
"We applied for the exemption on the assumption that we might not get it, they're obviously very hard to get and not everybody gets them and we're extremely grateful.
"Had they not they would have had to isolate at the facility."
He added they would be more than happy to foot any extra costs if required.
The 33-year-old's family travelled with him to Melbourne prior to the start of the Australian NBL season, where the team was to be based. However, due to a Covid-19 outbreak in early January in Victoria, the club was forced to move again, this time to Hobart.
Abercrombie's wife and children then elected to return home. They were greeted by an isolation facility that he says was "concerning".
He admits in hindsight that complaining on social media was not the right first step to take.
"Given the situation again I don't think that was the right way to go about things. But it was an emotional and stressful time for my wife, we literally had two hours to pack our bags in Tasmania, get on a plane in the next two hours and she flew all the way back to New Zealand from Melbourne on very little sleep.
"If she had her time again we wouldn't have made those complaints public, but also the situation she was confronted with in managed isolation I don't think was appropriate for any family or individual arriving with mould and things on windowsills where potential viruses could live."
Last month Abercrombie told NZME – after moving to Hobart – he was concerned the duties of looking after three children could be too much work for his wife while away from their usual home.
Quarantine issues are just another fire Abercrombie is having to put out, in what is turning out to be a trying start to the NBL season.
He and his Breakers teammates have had to battle ongoing Covid-related issues since arriving in Australia.
The club was forced to remain in Adelaide last week following their first two games of the season due to players feeling unwell, leading to precautionary testing and remaining in South Australia.
They have since been cleared to return to training, and next play the Cairns Taipans on Saturday.
