"Is that ideal? Maybe not, but look, it's good. At least the referee isn't the same guy who did Hughie Fury's last two fights.
"I'd like to acknowledge the compromise which we'll accept. And to be honest, the officials are going to be under scrutiny anyway because of all the fuss."
Currently there will be two American judges and O'Connor, an Englishman. But there was still a possibility a New Zealander could replace an American on the judging panel. That was with the WBO, Higgins said.
"The most important thing is a balanced panel. If there was a Kiwi to offset the Brit that would be fine," Higgins said.
Parker's trainer Kevin Barry said: "My focus has never been the officials but I applaud the British Boxing Board for listening to David. Dave did a really good job getting the referee changed. We have not got neutral officials but we did not like the ref that we had. I believe he is now one of the judges.
"It was good work by this team to get this through. They were standing pretty steady over the last week to 10 days, saying 'these are going to be the officials, this is the referee, so lump it'. Well, we've got it changed."
Parker v Fury at Manchester Arena will be shown in New Zealand live on Sky Arena from 8am on Sunday for $39.95.