Do you have camera's in the cabs of the elevators? If you don't I would highly recommend them, it keeps everyone honest especially when it comes to vandalism.

To answer your question; yes, people jumping in the car can cause the governor switch to set and trap people. This would be something every elevator company would bill for, as this is not a failure of the elevator.

I have a large student housing building where after bar time the students found it funny to all jump at the same time and shut the cars down due to the governor or load weigher faults. This was until the building started passing on our OT bills to the students which they identified on camera. After the kids were billed and the building put signs in the elevator with warnings, the issues stopped.