Ive always thought they might have a method to ignore the wake work if theres a specific frequency sent at the same time. I’ve noticed that there are sometimes TV commercials that have the “alexa” or “hey google” wake words, but they do not activate the smart speakers. But if the smart speakers hear something close on just a random tv show they will activate.

But as others have said, they might be able to just sleep the wake algorithm temporarily when they know it’s playing back its own wake word.