As limited as my knowledge of primitive consoles go, the 360's Red Rings problem is a result of the HARDWARE. Live has nothing to do with this; it is a multiplayer-based SOFTWARE program that allows you to play with many people online.
You show your dumb*%$ brother this and if you want, I'll go tumble with him a little
Freakenstein is right, the red ring of death is related to hardware failure or the UV cable being unplugged, unless software is managing to intentionally damage your hardware, which no packaged and retailed product would, then you there should be no correlation between the games you play or features you use and the state of the hardware.
Some games are good without Live, like RPGs (not that there's many quality ones being released these days - damn publishers), but if you're more into the games that require Live tell your fool of a brother that regardless of whether you're playing over a network or alone, the hardware is still going to blow up or fail completely at some point.
