We know they are streaming it to do all the NLP in the cloud. This is obvious from the computational costs alone of doing NLP.
The important question here is "What happens to the audio data streamed to the cloud, a few seconds AFTER the query has been identified (or not identified) and the results sent back to the Alexa device?"
The nieve assumption is "all audio data is deleted after processing". The reality is that data is still valuable to Amazon for a variety of uses such as
(1) further training their voice recognition software
(2) advertising data mining [how many people are in the room, things they are talking about --- note, Facebook's mobile app infamously does this]
If they just store the query text, that is 'best case' from a privacy perspective. If they just store query text and query audio, that is less than ideal, but not too bad. If they store all audio, ever recorded, for an indefinite period of time... that is what this police request could reveal: Audio data stored for a non-keyword-trigger, and for days/weeks after the fact.