Surely it's possible to sniff what's being sent back to Amazon's servers? If Amazon are lying and they are storing/analysing everything the Echo hears, surely this would be easy to prove?
However, this line of reasoning can be refuted all the way down to being impossible to prove/disprove. For example, there is reasonably an audio processing chip in Alexa that does always-on keyword listening, and it's possible it could track breadcrumbs over time (e.g., voice fingerprints, triggering keywords like "bomb", etc). This data can then be interlaced with innocuous data, for example inside an access token (opaque blob used to identify on whose behalf the Alexa is making requests). That would make it virtually impossible to find even if you had full access to the network traffic.
Anyway, when it comes to these things I like to take an Occam's razor approach. There's a great number of things a company can do to spy on you, but most likely when it comes to mass surveillance it's easier to tap into more obvious sources of data like your browsing history from the ISP, your phone line, Facebook/Google tracking data. In fact, I'd be more scared of say Facebook's and Google's voice assistants than Amazon or Apple because the latter two don't depend as much on consumer identity as a business.
EDIT: Another thing that just came to my mind. Even when you analyze network traffic and observe that traffic only occurs during your queries (i.e. in the seconds after the hotword is uttered), that doesn't mean that the Echo won't use the opportunity to send some previously-recorded audio to the server together with the current recording. In the same way that clever hackers disguise themselves by having their network traffic mimic the shape and direction of legitimate network traffic.
Now, there is some security basis
http://www.cs.unc.edu/~fabian/papers/tissec2010.pdf
>Uncovering Spoken Phrases in Encrypted Voice over IP Conversations
However, if you don't mind potentially destroying your echo, I'm sure you could reverse engineer a way to see what's going on.