That doesn't necessarily mean that any word is an option, just that your set of options is larger than 1.

Isn't this patently false?

If it's not listening how can it hear the wake word?

Xbox and google now do the same thing. As I understand it all the sound is filtered locally for the keyword. If it's detected, then it starts recording and sends the audio to a server to be processed.

Now they just need a Paul Bettany voice pack.

That's pretty good, but it's second place to my desire for a Majel Barrett voice pack.

Funnily enough, Google Now's voice search was originally called "Project Majel" for that reason - https://en.wikipedia.org/wiki/Google_Now#History