Not a huge stretch at all. The police are, even now, attempting to get Alexa recordings from Amazon in connection with a murder investigation in Arkansas... Alexa hears all and sends the voice data to Amazon servers where it is kept, virtually forever on backups of the server's data. You can "mute" the device, but, then you have to walk over to it to reactivate the microphone...kind of kills any advantage the device has.
It will be a really long time before I invite big brother in to live with us. We all use devices that can have their data hijacked, but, for the most part, you know when it might happen and can behave accordingly. Alexa records everything it hears and sends it to Amazon, nothing "selective" about it. If you just can't live with using the remote to turn your tv on, or, you can't be bothered to look at the weather app on your smartphone, then Alexa may be perfect for you. Just don't put it on the nightstand by your bed :B