I posted the same problem in another thread recently. Someone has since said to me that the running boards are probably an aluminium alloy. If they could be got off the vehicle easily and separated from the plastic 'studs' which protrude through the metal, then the boards could be repolished and relacquered.
I don't know if anyone has ever done this or if the boards can be separated so I'm going to try some metal cleaner in the meantime.
I have a feeling that BMW didn't use a very durable lacquer when they made these boards. Whether or not this is universally recognised by BMW as a warranty replaceable item will be interesting to find out.