> Does ownership of the network override the laws of the country the network is in?
It's not a legal question at all. If you use the service you have accepted their terms and so have given them permission to do this.
> If they had opened physical mail, this would be a criminal charge. But because it's digital, somehow ownership of the service exempts them from having to obey any kind of privacy laws.
The fact it's digital doesn't make it a special case, if you agreed to let them open your physical mail they could do that too.
> Dangerous and shows why you should not trust anything online.
You shouldn't trust anyone on line, that's true. However this isn't the best example of that, but it is a good example of why you should read the T&C of anything you sign up to.