I agree, it doesn't work that way. Microsoft was impressed with Peter Moore and his connections he made in the industry. Peter Moore had massive respect (listen to the interview, he literally names Japanese developers by name that created big Dreamcast games and names niche games even 15+ years later) for the talent at SEGA.
Its not surprising that when SEGA went 3rd party and he went on to Xbox that he would persuade Microsoft to try and workout a exclusive deal with SEGA. You got to know, even tho Dreamcast was a failure in Japan and didn't do amazing in Europe, it had a big fanbase of hardcore gamers in America.
We did a podcast with Gary Johnson (Toejam & Earl) and he said the contract for exclusivity was basically Microsoft paying the advertising or something to that effect. Which seems like a win for Microsoft on both fronts (more exclusives getting ad = more advertising for your console).
Hard to know if signing a exclusive deal is a good idea at the start of a console generation. See Sonic on Wii U for example, they came off the massive success of the Wii and Sonic was a huge seller on Nintendo platforms. How'd they know the Wii U will flop and signing the contract was probably a bad idea. I guess it didn't help that Boom games were shit and Lost World left more to be desired.