That’s not the main problem. It is more like an excuse. The main problem has been explained in the video right before that:

Their radar is bad at recognizing immobile cars on the road. This means all objects. All obstacles on your road!

The emergency vehicles just happen to be your most frequent kind of obstacles.

The fallback to the camera is a bad excuse anyway, because radar is needed first to detect any obstacles. The cam will usually be later (=at closer distance) than the radar.

The even better solution (Trigger warning: nerdy stuff incoming) is to always mix all results of all kinds of sensors at an early stage in the processing software. That’s what european car makers do right from the beginning, but Tesla is way behind with their engineering. Their sensors still work indepently, and each does their own processing. So every shortcoming of one sensor creates a faulty detection result that has to be covered later (read: seconds later, not milliseconds) by other kinds of sensors.