They say that because PS2 had a mountain of 3rd party exclusives, and Xbox had a large 3rd party exclusive library as well. What those people don't get is that Nintendo's crappy mini-disks were preventing the lion's share of those 3rd party PS2 exclusives from being on it. Had Nintendo had disks that could have held the entire games without disk swapping those games would have come to GC. And those 3rd party Xbox exclusives were made for PC and easily ported to Xbox, because Xbox was basically a computer like most modern consoles.
That's just outright wrong because most games during that generation didn't even exceed file sizes of 1.5 GB. And those that did, could have been reduced in size to make them fit on a single disc if two discs were not wanted.
The primary reason why Nintendo didn't get those PS2 exclusives is that Japanese developers at large were not interested in doing multiplatform releases, hence why the Xbox missed out on much of the same games. American and European publishers have had a multiplat approach since ages, but the only thing that could change the Japanese stance was the failure of the PS3. During 2007 and 2008 there was hardly any month without news that an exclusive in development for the PS3 was going to go multiplat.
When you look at games with lower development costs, exclusivity of Japanese games remained much longer and was common on the 3DS up until the end of its life. If it's financially feasible to develop for only a single platform, then that's still what Japanese developers prefer.