He denied the allegation - raised by some Australian media - that Bromwich had initially offered to stand down from the team, before Kidwell insisted on making the announcement himself.
"I don't know where that has come from," said Kidwell. "The process was I made the decision and I spoke to Jesse and Kevin, they were the first two people I talked to."
Kidwell also offered no guarantees that the disgraced pair would return after the World Cup, though hinted that it was more than likely.
"I'm concentrating on the World Cup at the moment," said Kidwell. "They are doing the right things with their clubs and I'll be in close contact with them. They are really good men who have made an out of character mistake and we have come to that decision. We'll move forward and deal with that after."
The more pressing goal is the clash with Samoa in Auckland on October 28, which is the first opportunity for the Kiwis to restore their battered image in their first game on home soil since the 2014 Four Nations.
"There's a long way to go to make sure we do the right things off the field with the community and win back [the] New Zealand public," said Kidwell.
"I suppose playing tests here throughout New Zealand will go a long way to get them back. [But] they're rugby league fans, they love rugby league and they want to see the best players out there playing with passion and with heart."
Kidwell said that the quartet of Simon Mannering, Adam Blair, Shaun Johnson and Roger Tuivasa-Sheck are the prime contenders to replace Bromwich. Kidwell also confirmed that Cowboys coach Paul Green has ruled himself out of contention for an assistant coach role.
"As far as I know he has made himself unavailable," said Kidwell. "He was one of the candidates I reached out to and there's a couple more that I'm in the process of going through."