The only contract with the customer is the privacy policy. The privacy policy is just a promise from a site to abide by certain rules. In the case that there is not a privacy policy, then whatever you tell that site can and will be used against you. From tracking cookies to the most sensitive of files, if you are providing information to a site then you have to assume that it will be used in any way the company sees fit unless they promise otherwise.
Ethically there may be different obligations, but to say that there is some implicit "contract with the customer" is simply not the case.
I feel it is safer and more realistic to presume the first paragraph I wrote is the case and cover yourself with a privacy policy if you want to do otherwise as I mentioned.
As always, ask a lawyer if you want professional advice.
If you do want the right to spelunk through customer data, you need to declare that in the privacy policy. If you declare otherwise, you're breaching the contract with the customer.
The problem is that incidents and attitudes like this make the market lose trust with the cloud services industry, which is poison to everyone.