So, reading through the VentureBeat article, I get the following impressions:
1.) Based on everything I've seen on Bungie, they have a work environment that encourages people to be incredibly proud of their own work and view their workplace as a cult-like entity whose integrity must be protected and worshipped. Given this, I'm not surprised Marty was very concerned about his work being shown and felt that Activision changing the trailer music was unacceptable. Bungie at least somewhat agreed seeing as they sent in a veto. Activision, having given Bungie a really sweet deal and spending a very large amount of money on the game, wanted to assert that they were in charge of marketing and denied Bungie's request to change it back. This is reasonable from their perspective.
2.) Marty self evidently wanted to either get his way or leave. Since he had what was likely a multimillion dollar incentive to get fired instead of leaving, he threw a major tantrum at E3. Activision obviously didn't care about his music, and Marty was okay with going out the door, so Bungie was the only one with something to lose here. This is where I feel they messed up. After E3, they should have either just fired him and gave him his money, or worked on some type of conciliation with Marty where they promised him an album release, future trailer music, concerts, or whatever. Telling him his behavior was unacceptable was fine (because it definitely was), but just leaving it at that instead of following up with one of the other options was incredibly dumb.
3.) At this point, Marty just wanted to go, but Bungie didn't want to fire him given he'd take a bunch of money with him. As such, he sat there being an obstructionist and not doing his work in an effort to get fired, and they let him do this for a year. Their original contract heavily incentivized this type of behavior, and their unwillingness to act caused them a ton of unnecessarily pain.
4.) When they finally fired Marty, it was clearly the correct choice. They should have given him his money though since he had a rock solid case against them, as this ruling shows. Instead, they got a year of expensive legal drama and bad PR, so they hurt their own reputation and spent even more money than they had to.
Now, everyone comes out of this looking worse for the wear, but Activision and Marty don't really have to worry about it since the former already has a terrible reputation and Marty is only ever interested in working with his four person studio at this point. Bungie on the other hand wants to hire 100s of more staff judging by their job page, and this reflects really poorly on their work environment/management (ir)responsibility.