Yes. I can make mine replicate this. When it happens, the "top" of the button gets stuck under the plastic of the gear shifter. If I press a few times more towards the "bottom" of the button, I can get it to pop out.

If you're at any real speed, it does nothing. But as you slow down to a Park-able speed, the solenoid inside will actuate non-stop thinking that the button is being pressed.

I now press the button towards the "middle" or "bottom" all the time to use it. I've instructed my wife to do the same.