Indeed, if you keep your usage within the tier of usage that is free, they charge you exactly $0 per month. It is only for usage beyond that free tier that you are charged.

They should shut off your service if you go over the free tier, and all of these problems would disappear.

I agree that there should be an option for a user to select "I never want to pay so much as $0.01 and if there is a circumstance where I'd need to, I expect you to shut off my services and delete my data if needed in order to avoid me incurring any bills."

That would solve this issue, but needs to be an explicit opt-in, because a lot of users don't want that.