That's the gist of how it likely works; the wake word is detected by an "always on" audio DSP, but a software mode prevents the passing of microphone data back up to the SoC. I'm actually quite familiar with Amazon Echo engineering design, and they implement the "mute" feature in a manner that takes privacy seriously: the LED indicator on that button is hardwired to only turn on when the microphone is literally powered off. Thus, an Echo device can't even manage such a cheeky response, nor can a software bug or hack enable listening while the mute button is lit.