I know it seems like rumors, but they seemed pretty certain about it.
Sawyer did not leave Black Isle with the other Obsidian folks at first, he stayed and kept working on Van Buren until it was canceled, BUT regardless, I asked some more:
So Mitsoda was one of the few let go when the Fallout Fantasy project was ended (in 2001, I think?). I don't know much about this project.
When Fallout 3/Van Buren was hiring writers and designers (once Fallout 3 was becoming a reality after BG3: Black Hound was axed in 2002, I think, and Black Isle suddenly was without a project so they everyone was moved on to Fallout 3/Van Buren), word is Mitsoda was one of the ones who applied either on his own (before he went to Troika) or from Troika, apparently (although I suppose it's possible he re-applied after the layoffs from the Fallout Fantasy project and if rejected, went on to Troika and if so, good for him), but he did apply at that time and made it to the final round of applicants.
But that said, they were pretty clear Sawyer's firm no on Mitsoda caused him to get rejected from the Van Buren/Black Isle applicants. I don't know who was hired in Mitsoda's place, but it didn't matter much I suppose considering it sounded like the Van Buren game was on the chopping block because it was PC-only even before the team knew (if it had been something that could have gone to consoles, then it likely would have been kept and continued to try and be funded).
At Obsidian, you're right that Sawyer came after Mitsoda, and I don't think that was the situation at Obsidian for the reasons you state. It also doesn't sound like they worked on the same project when they were at Obsidian (or at least not primarily). Chances are that without Sawyer there is what allowed Mitsoda to be hired since Sawyer was out of the picture. BUT asking more:
Sawyer was the one who prevented Mitsoda from remaining at Obsidian once Mitsoda was being removed from Alpha Protocol - the approach internally was since Mitsoda wasn't working out on Alpha Protocol with the "organizational changes" and restructuring on that doomed title (Mitsoda "not working out" apparently was a judgment by the executive producer, whoever that was, but it was said that it was because Mitsoda wouldn't do any narrative changes and resisted changes to the old script despite the overhaul of the game), it was still felt Mitsoda might be able to move to Obsidian's other project (I think this was Aliens?), but it turned out the team (headed by Sawyer) had already intervened with the executive producer and said they would not want him on their project, so he had to leave Obsidian completely. It sounded pretty rough.