The first thing you should do is remove the 2 wires from the wall button on terminals 1 and 2 on the opener. Make sure all the other wires are still connected. This will eliminate the wires and the wall button itself. Sometimes the installer uses metal staples and they cut through the insulation and cause this problem. Sometimes the wall button is bad especially if there have been teenagers who slap it rather than press the button. Give this a try and post back.

I have the same problem. It doesn't seem to be the wall switch. Can outside influences activate the remote?

Newer openers have basically eliminated the outside influence. It is usually the wall switch, wiring or mis-adjustments.