I think you've answered your own question.

I agree with Chuck's advice...

The deal you make withe the devil/dealer when you buy that warranty is "I will always use the same tires".

Tire is free, put it on. Buy 4 new tires. You will not have a BMW tire warranty on those new tires I assume. (since they are not an OE tire for that rim, correct?)

You could save the old, good tire as an emergency spare, or sell it...

A