Here is what I believe happened:
Rare was working on Dinosaur Planet for N64, but Nintendo had them use Starfox instead, because of the similarities between the main character models. It seemed like vaporware, but later reemerged supposedly as a launch title for the GCN, however, it got pushed back because Rare was having a problem meeting the deadline. Then as their second deadline of February came around, it still wasn't ready. So they had another deadline for April, each time announcing it as official to the public, meanwhile, GCN had hardly any games to fill the gap from launch to the next holiday, much less any titles that would make GCN a must have. Nintendo needed every key title they could get to fill out the remnants of GCN's very modest launch.
At the time, Nintendo was still run by Yamauchi, not a very forgiving and arrogant man, despite the greatness of Rare. This is the same guy that told Square to shove it over the CD medium of Playstation and was in charge of the Phillips/Sony fiasco, as well as forcing developers to pay tons of royalties during the last high point of Nintendo's past. Perhaps Nintendo sensed Rare was different before Rare began splitting apart. Maybe they began splitting apart before Nintendo noticed the difference. Regardless, the rumors of Rare getting sold started and several Rare employees had already begun to jump ship, Mark Hollis to form Zoonami and some other key figures to Free Radical, specifically those involved heavily in the design of Goldeneye, Perfect Dark, etc.
Then Microsoft agreed to buy Rare, but StarFox Adventures still wasn't finished. When it finally released, it was riddled with rushed glitches and coherence issues left over from the transition from Dinosaur Planet to its StarFox alter ego along with a save issue or two. Plus, many of the puzzles seemed to be straight out of Zelda. I think part of this is due to Nintendo's teams taking over much of the project during the completion of StarFox Adventures, so that it could finally get to store shelves for that next Holiday, an entire year behind its very sensitive original release date.
Rare was left a shell of its former self and was unable to function like it once had. I believe this adequately explains one reason why Kameo and Perfect Dark Zero, who many Rare fans bought an Xbox for, didn't show up until Xbox 360 a whole generation later, why Perfect Dark Zero had a bit different art design especially at the first unvealing, why Timesplitters plays so much like Goldeneye and Perfect Dark, and why the biggest title Rare had for the Xbox was a remake of an N64 game, Conker's Bad Fur Day, with updated graphics and a few add ons.
I would say that Microsoft realized during the Xbox years that they got a bum stick with Rare and needed to rebuild them into a somewhat new team.