Can the device monitor for other words that trigger other UX sequences? Of course it can!
Can Amazon deliver an OTA update to this network connected device to change behavior after it leaves the factory? There is no reason to believe that they cannot.
So, no, I don't believe the police are wrong here. In fact, I would be in favor of law enforcement having the ability to "tap" these network-attached microphone appliances with a warrant. Then, perhaps, people will begin to understand what they've really bought.
EDIT: Passive monitoring ("listening") is not the same thing as storage ("recording"). In some cases below, these are being conflated.