It is illegal in Texas to capture, posses, display, or use images or video from drones taken of private property or people on private property without permission or other limited authorizations (active pursuit of a suspect, investigating crime scene, search warrant, some licensed real estate activity, etc)
I don't know what laws in other states/countries are, but I would guess many have something similar that would prevent that.
Google recently agreed to a ~1.4 billion dollar settlement with Texas for privacy violations. If company is big enough to do mass drone delivery and wants to not only break the law but also lie about it, good luck to them I guess.
Sure, they can say the cameras are for "obstacle avoidance" all they want, the camera is on? Well, they just captured and used images/video of everyone's private property to get to that delivery and did so with intent. So they might have permission from the one person getting the delivery but they don't for the hundreds of others they past, and I would not want to get that settlement bill in the mail.