2001 factory alarm: going off by itself

Occasionally while the truck is parked and locked, the alarm will go off by itself. Sometimes after I unlock the pickup with the keyless remote, the alarm will go off when I open the door. Just last evening, the truck was in my garage. It hadn't been driven for several hours and it was not locked. But the alarm went of while nobody was in the garage (garage door was down). It shouldn't have; the alarm shouldn't have been enabled. In all cases, inserting the key into the ignition and rotating the cylinder stops the alarm and its fine after that for several days/weeks/months.

That it wasn't locked makes me think it's a body control module problem. Anyone have this type of problem? Any ideas aside from replacing the BCM?