Timed exclusivity SHOULD matter, but apparently it does and it doesn't.
I remember people making a big deal that Splinter Cell sold better than Metroid Prime at first, even when I was pretty sure it was common knowledge that Splinter Cell wouldn't always be on just the Xbox. In fact, it would even make it onto the GameCube.
People make a big deal about Final Fantasy and consider it a PlayStation franchise. But the PC soon got VII & VIII, and it even got XI shortly before the PS2 did, and later XI also came to the Xbox 360. Excluding the side story games and spinoffs, that means IX is the only PSX one, and X and XII are the only PS2 ones. That's three games out of twelve are actually exclusive, that's only a quarter of the main games. It could be less than a quarter since XIII is not guaranteed to stay on only the PS3. How does one-quarter (or less) of a franchise equate the franchise with one brand of consoles? (In fact, half of the series debuted on the NES/Famicom and Super NES/Super Famicom!)
By that logic, Nintendo should be the home of Metal Gear, since it has the original Metal Gear and the definitive version of Metal Gear Solid in the Twin Snakes version. Sure, we don't have Sons Of Liberty, Snake Eater, and are unlikely to get Guns Of The Patriots, but even if we counted the "real" Metal Gear 2 on the MSX (which I don't think the PSX has any version of), Nintendo has one third of the Metal Gears. If one-quarter of FFs is exclusively on the PlayStations and known for it, it's actually less ridiculous to claim Metal Gear as a Nintendo franchise since Nintendo has one-third of it. (Well, Snake IS in SSB:B, which actually came to me as an afterthought to this point.)
Timed exclusivity, but moreso marketing and the prospect of future sequels, is what destroys what I think should be pretty good logic above. You hear more about a game when it's new, so when FF VII and FF VIII were hot on the PSX, that cemented it in the minds of gamers that modern FFs somehow "belonged" there - and most (stupid) people didn't care about pre-VII FFs. The Twin Snakes was well after the original MGS which was revolutionary at the time and the GameCube wasn't getting any sequels so everyone believed the PlayStation was the place for MGS, disregarding the PC ports of Solid and Solid 2: Substance (which also ended up on the Xbox).
Viewtiful Joe and RE4 are a different story - the PS2 was too far ahead. I still think it was pretty idiotic for Capcom to announce the PS2 port of RE4 just BEFORE the GCN version came out. Dumb, dumb, dumb. RE4 was on everyone's radar, PS2 fans were considering GameCubes just for that, then while they have everyone's attention, Capcom goes "oh, don't worry, we decided to put it on your beloved PS2s as well." Timing came into play there too.
No one operates on pure logic, unfortunately, so mention FF and even you would probably still think "PlayStation", not "PlayStation and PC". Mention MGS and you will probably think "PlayStation", not "PlayStation and Xbox and GameCube and PC." But, mention RE4 and you will probably think "GameCube AND PlayStation 2" and not just "GameCube". Sheesh.