Interesting... I just checked my manual and there's no mention of a red dot key. Just a flat (for the wallet), valet and master key. It can only be armed by the flat or master by locking the either front doors or the trunk. It will sound if the doors, trunk, or hood are opened - or if the radio is removed or brake is depressed.
I guess the red-dot just refers to the master key and they changed the "lingo"...
Nonetheless, it sounds like you solved the problem.