I think the vast majority of people are completely misunderstanding this whole thing, in that I believe she DID mean the actual microwave oven is what's spying on you, and that she IS right about it, just not in the sense that it sounds at face value.

In one of his rants on his show from a day or 2 ago, Alex Jones mentioned the comment from whoever it was at the CIA from years ago talking about how they'll spy on you through your dishwasher. A dishwasher sounds as crazy as a microwave, because why would they have cameras or microphones built into them? The answer is they don't- but they have circuit boards to operate all of the electronics in them, and on those circuit boards are various chips that can be tuned to various radio frequencies and pick up a variety of things. That captured signal can then be transmitted through the electrical line, since the device is plugged in for power already, and once it's tapped into the power grid, it can be sent anywhere. Sending data over electrical lines is easily possible of course, even for consumers via powerline adapters.

That's how these seemingly innocuous devices are able to spy on you without needing its own camera or microphone. So YES, that device is spying on you, it's just that it's piggybacking off of something else, like the phone that you have next to you at all times.