Actually, it isn't false. halo was the ground breaker for Xbox that Mario 64 ws for N64. just like Mario64, if that first game wasn't made, it would be likely that that system would have never taken off.
Also, allow me to freely break down what series is famous for what system producer if I may as far as I know
Sony: .hack, tomb Raider, Digimon (switching sides), Xenosaga, GTA, FF, devil may cry, jack and daxter, rachet and clank, Sly Cooper. That's all i can think of for now.
MIcrosoft: halo, Fable, Tom Clansey, and again, all I can think of.
Nintendo: FFCC, Mario Bros., Donkey Kong, Zelda, Star Fox, Fire Emblem, Sonic (for now), Pokemon, Advanced Wars, Megaman Battle Network, yugioh, Digimon (claiming from sony), Animal Crossing, PIkmin, Metroid, Earthbound, Early FF games(Which are in the remaking process), F-zero, Kirby. All I can think of for now.
If you think my listing biased, keep in mind that Nintendo was an established game maker before they even made systems. Plus they've been making games long before both Sony and microsoft. So of course they'd have a longer list of established games. :\ And the reasson why these matter is because a lot of these are currently being remade or enhanced to be played on Gamecube or GBA. Most of them already are.