My car has a pushbutton "ignition switch" and i have not tried pushing it while travelling; however, my lexus also has floormat retention to stop the floormat from going onto the gas pedal. It wasn't "accidental" - there was a recall. The toyotas and lexus affected don't have a floating accelerator pedal, where it hangs from above and there's space underneath. The gas pedal is hinged on the floor, and swings free at the top. So you could shove something forward and it will push the gas pedal down.

If memory serves there was an instance in southern california where the driver called 911 or some other recorded line (they died); but it may have just been a witness statement i remember.