> I know nothing about the supply chain for car radios, but I wouldn't be surprised if it was all made by some secondary supplier, so Mazda doesn't even necessarily have the code to the section they need to patch.

You are correct that in general the automotive OEM's farm out the various components of the vehicle to suppliers. In that case, they probably also have some sort of support contract in place that ensures the supplier will address issues like this in a timely manner for the duration of the warranty period for the vehicles it is included in.