The company doesn't go into to too much detail about what the fingerprinting involves, but it stems from a command filtering patent. For the Super Bowl ad and other promos where Amazon already knows what's coming, Amazon will send fingerprints in advance so Alexa can compare input and ignore requests from ads. In situations where Amazon can't predict what will happen (such as a TV segment), it uses dynamic fingerprinting that looks for many simultaneous activations based on the same audio. This won't catch every false request, but it typically stops "80 to 90 percent" of devices from responding. Let's put it this way -- a funny incident shouldn't devolve into national chaos.
Amazon has another technique where it can send an inaudible signal to stop Alexa from responding, although that doesn't appear to be in use here.
Unfortunately, the patent suggests that other companies will have to find other ways to screen for unintended input. And that's unfortunate -- just ask anyone who's had a phone go off when a show says "OK Google" or "hey Siri." However, it's good to know that companies are just as annoyed by false responses as you are.