Yes, I gave them the VIN right from the start. I thought the dealer was blowing smoke up my butt, but now I see they need to see the vendor stamp on the back of the wheel to make sure the wheels match.
In my decades in manufacturing, we *never* stocked a non-direct replacement part under the same part number as a direct-replacement part. Maybe Mazda didn't either, but the on-line sellers don't seem to realize that...