Yeah, Echo is a good listener. In fact, when I ran the video on the OP's site and he said "Alexa, what time is it?" my Echo in the other room woke up and told me the time :)
It would also be interesting if you could create sounds that sound like commands to the algorithms, but are not easily recognizable for the user.
e.g. you could do it by buffering the request, checking and submitting once you're confident about authenticity, but then you'd be delaying submission and response, depending on how much you'd need to buffer to gain sufficient confidence that the individual is authorised.
It's not "secure" in any sense, but it cuts down on false positives and perhaps some very juvenile hacking attempts. Any professional hacker will generate a close-enough voiceprint that you can't use voice recognition inherently (purely passively) as authentication any time soon.