[LogicalApex]

I've been pondering this one for a bit as it is very concerning!

The only two scenarios I can possibly think of that could cause this... One with a floor mat and another with Cruise Control (CC).

In both scenarios I can think of the car wasn't in P, but was brought to a stop with Auto H activated. When you've stopped the car in this manner it will show PARK in the instrument cluster, but the subtle difference is PARK will be illuminated green instead of red. The parking brake will be activated, but Auto H will automatically disengage it when it is no longer needed.

The secondary condition would be a floor mat shifting up and then pressing the accelerator. Auto H would disengage the parking brake and accelerate...

The other would be the car previously being in CC and since it was brought to a stop and parked via Auto H. The CC can be reactivated by simply hitting "resume" on the steering wheel and the car will attempt to come up to the previous CC speed very quickly. It will also automatically disengage the parking brake in this scenario.

The only way I could think R would happen in either scenario would be accidental engagement when attempting to get the car into N to stop its unintended forward momentum. Grabbing the shifter in such a way you press the button at the same time could cause that issue.

If the car truly did go from P to D with no human intervention at all you should log a complaint with NHTSA and press your insurance company, BMW, or NHTSA to get the cars black box pulled so BMW can be forced to issue a recall. As that's an extremely serious safety issue.