This isn't an actual subpoena - a subpoena is an order issued by a court, and requires probable cause. What's happening here is that the cops are asking Amazon for the data, and Amazon is giving it to them, without being legally obligated to do so. Assuming that the user's terms of service say that Amazon can do this, they don't need your permission to do so, or any proof that a crime has occurred.
I assume it's legal for Amazon to give them these videos, since the images they're asking for are things that the cops or anyone else could have seen happening outside your house if they would have been driving by (or that your neighbors could have told the cops). There's no legal expectation of privacy, as there would be inside your house.
I assume it's legal for Amazon to give them these videos, since the images they're asking for are things that the cops or anyone else could have seen happening outside your house if they would have been driving by (or that your neighbors could have told the cops). There's no legal expectation of privacy, as there would be inside your house.