One of my coworkers told me he previously worked on the motherboard team for Intel and was regaling the office with stories about testing the motherboards against the latest games. Apparently many of the Intel engineers personally tested overclocking the processors to see how much they could take before they fried.
At some point I asked him if he knew anything about the Management Engine. He said that they were starting to become a thing right around the time he was leaving, so he didn't know too much about them. I said, "Well, there's a bunch of paranoid people that are uneasy about it because, to my understanding, it's a blackbox second processor and we really have no idea what it's doing."
Without prompt, he replied, "Oh, you mean like the FBI using it to listen in? Yeah, that happened. It happened on AT&T's when I went over there as well."*
That's my story. I apologize if it looks like I'm spreading FUD here, since I'm not going to give up my name or my coworker's to verify the story, but I sincerely doubt that Intel would acknowledge such a capability anyway, so, take it as you will. Libreboot, the Management Engine cleaner, and other such projects need to exist. My coworker's comment convinced me of that.
* I'm not sure what he's referring to here. Maybe someone else can shed some light. Does AT&T make processors?