Frank,
Reading about the problem you are having made me think of two things...first, do you drive a vehicle that has an overhead console with a feature that permits you to operate your door opener using the vehicle's pushbutton? Our two GM cars have this and we don't use the remotes that came with the openers as supplied. I took the batteries out of those so they would not operate the doors after I shoved them into our junk drawer.
Second, do you have one of those keyless entry systems that operates the opener from the exterior of the garage? They can be either wireless or hard wired type. Back in 1989 I installed a new Stanley opener in the garage and also added a hard wired keypad, being exposed to the elements finally shorted out the electronics and it started opening the door on it's own. If you have such a keypad try disconnecting it's power to see if that item is triggering the strange behavior.