...it's happens all the time in the business world. Allows them to save a little face and when applying and interviewing for a new job. They can avoid having to be honest about getting fired at their last job (and having to explain it). Bottom line doesn't change, when the day is over they weren't wanted and no longer have a job.
In Anae's case, iirc I remember reading an article or something online where Bronco had hoped to shake up his offensive staff and demote Anae to OL Coach and demote Mark Weber to a different position coach but Weber didn't want to take a step down and obviously (if this is true) Anae didn't want to either.
There's a lot of hair splitting and dancing around on fine lines, it's reminiscent of Bill Clinton's testimony before Congress in the Lewinsky hearings, "I did not have ...."