The high octane requirement of our engines is due to their higher compression. The more you compress gas and air, the more likely they are to pre-ignite. Ignition just from pressure and heat, before the spark. That is pinging , knocking or detonation that everyone talks about. So.........the use of 91 or higher in our engines will help prevent this pre-ignition as the higher octane gas has a higher ignition temperature, so in our high-compression BMW engines, this is a must. Also, the same applies to all high performance, hence high compression engines.
Correct me if I am wrong.
BTW I agree that the one tankful of 87 will not harm your car as the ignition will be retarded as the engine senses the pre-ignition that WILL occur, but you won't get the full performance BMW intended and spent those long painstaking hours designing into your engine when your spark is retarded to compensate for the lower octane fuel.