That's never been verified. It was more of mutual parting according to them unless Booger's drunk in public again.
For Booger to have approached him with that idea for the war room in their last draft has to tell you how desperate Booger was for attention, he's a child in that regard. For Wannstedt to have to talk Johnson into coming into the war room tells me how far that rift was becoming.
Then Booger gets drunk in public, evidently a habit, and wants some credit and to be toasted by Johnson's coaching staff and for them to shun him tells you just how much the coaching staff thought of Booger.
Other GM's do not step up and want to overshadow their HC's and they seldom share anything with the media. They understand the coaching staff is its own animal.
Booger saw Johnson becoming a media star and was so jealous he couldn't handle it. Add to this he caught all of the heat for firing Landry and the death threats for not signing Emmitt and Johnson actually gets the credit for Emmitt getting signed and in by the 3rd game.
Now, the seeds of this were sewn when they were roommates at AR and Booger was an OL and Johnson a DL. That team was all about defense and set the record for scoring and had 5 shutouts, the offense was there so we could go to the bathroom or fix a sammich. It truly was an amazing defense and just judging by Johnson's personality, I don't think he let Booger forget the D was the dog and the O the tail.
According to the SEC doc "Before They Were Cowboys", Booger was inspired by Switzer, just as Johnson, and wanted to go into coaching but the money wasn't a lure and he didn't follow his true dream. Johnson did and lived the dream at the highest possible level, college and NFL rings. I think Booger admired and respected Johnson but I think he was just as jealous of him. Because his accomplishments were public, Booger hit a gusher, no one cared.
When Johnson pulled that radio move before the Niners game, he took on legendary status in Dallas and that was just too much for Booger's childlike ego to handle.
The town was just not big enough for the both of them and Johnson wanted out anyway.