I think of it this way:
Had Nintendo kept Rare around, Rare might have already released their Kameo and their Donkey Kong Racing and their Conker and their Perfect Dark Zero. It'd have helped Nintendo out a bit. Not have completely saved them, but if even 2 of those titles were released, it would have helped Nintendo's image a bit. Spread the Gamecube's appeal a bit.
Microsoft came in at an awkward time to buy Rare, or really, The Stamper Brothers came in at an awkward time and decided to split from Nintendo. I think what had happened was that when Microsoft bought Rare, instead of turning them onto the Xbox (Since so many Microsoft investments kind of mirrored Rare's games, most notably Halo series : Perfect Dark series), they would give them some extra development time to focus toward the Xbox successor.
If the Xbox Next hits and Rare's games turn out to be a trump card in it's success, then Nintendo messed up by allowing a competitor to have a good leg up. It'd be misery for Nintendo to go up against the Xbox next coming off the strength of Perfect Dark Zero, which turns out to be the Xenon's Halo. More misery than they would have had to deal with if they'd kept Rare.