@KittySitter We read this article when it first came out and as another poster in this thread pointed out, the article makes it clear that Alexa is only “recording” the commands you tell it, so it can be more responsive with your future commands.
We are sitters and HOs. As HOs, we tell sitters (during the video chat) about our Alexas on the main level – that’s the only place where we use A to control lights and music. The rest of the house (including the sitters’ private areas) are all old-fashioned manual lights. No Alexas in those areas.
And heavens no, our A devices aren’t even set up for us to listen in. Who has the slightest interest in doing such a thing? Frankly, I don’t even know how that would be done but I am told by my better half that there is an announcement on your end if that kind of “listening in” is attempted.
Our sitters have 100% chance to unplug all the three units (which we show them), and we don’t mind in the least. 
As THS sitters and when we are guests in AirBnBs, we’ve unplugged and put suspect devices in closed closets. LOL!