Bronco didn't let all 5 coaches go to not retain some of them. There were clearly some chemistry issues with that staff that needed to be addressed. It's certainly possible that after Anae was let go that he reiterated his desire to resign (from the middle of the season) and Bronco asked him to stay in some capacity. That would make the reporter's summary of Reynolds' statement 100% accurate as of the date of the interview.
The mere fact that Bronco asked Anae not to resign (at an undisclosed point in time) has very little probative value in the veracity of the sentence Reynolds confirmed for the reporter.