If you have a flashable modchip, just use X2 4980 BIOS. It will disable Live when the modchip is on. You don't really need to worry about the bottom information at all.
For Xbox Live Aware games, you will have to create a profile for the game.
If this is a backup, and you have Live on your Xbox and using it with the modchip off, do not use your gamertag as your profile for the game. When you do that, the game will automatically connect to Live. Create a profile that isn't the same as your gamertag.
Also, for modded Xbox users with backups with Live compabilities, turn off auto sign-in in the MS dash. If it is enabled, the game will connect to Live no matter what your profile is named in the game.
Of course, a non-Live related profile will allow you to system link with X-Link or XBConnect.
No Xbox games will connect to Live when you load it, unless your profile for the game is the same as your gamertag or auto sign-in is enabled.
Another good idea is to set a Xbox Live pass code for your account. The game will ask for the passcode before signing into Live.
Some Live Aware games are:
Ghost Recon: Island Thunder
Rainbow Six 3
Project Gotham Racing 2
MotoGP 2