False. Xbox pretty much WAS a low end PC, down to x86 and all.
They were just lazy and wanted the Xbox to look better anyway.
And so was the Dreamcast. It actually ran Windows CE. That doesn't mean the games are automatically ported to PC with ease.
And the PC version game out over 2 years after the Xbox version, was developed by Gearbox (not a MS owned company btw), and I highly doubt anyone at that point cared about Halo PC edition looking better, as we were focused on when Halo 2, as it was announced before Halo PC.