Way back in the '50's, my father had one of the first garage door openers. The receiver was even a vacuum tube device. In those simple times, all the device looked for was any kind of radio waves on its frequency, and it would activate. Sidebands or harmonics or some such thing from aircraft taking off from LAX would trigger that garage door.
Today, the door openers almost always require a digital code to be transmitted and identified by the receiver. It's like the difference between a simple latch, and a lock that only opens with a key.
First, make sure that yours is the type that uses a code. If it is, try changing the code. It could be that sombody else nearby has the same code. If it still opens on its own, try disconnecting the receiver for a while. If it still opens on its own, you have an intermittent short somewhere in the other wiring to the opener. If the problem is the receiver, get a different make.
There's absolutely no way that the actual motor or any of the mechanical parts have anything to do with it.