You certainly can't be sure of that. In fact, it is almost certain that these companies provide the data they collect to the police and government agencies data, often without warrant.
I'm not an asshole so I cancelled my subscription.
If other people are cool with doing things without any reasons and based on pure trust, that's on them. But that's not gonna be me
Consider the Nancy Guthrie case. The owner wasn't around to give consent, and the camera didn't even have an active subscription, yet law enforcement was still able to recover video from Google's systems.
The only way it could be as you say is if the video was only stored locally without any remote access, or if the video was encrypted with keys only you control. Google clearly is not doing this. I really, really doubt Amazon is.