The problem with this position is that the 4th amendment is not, and never has been an absolute right to privacy whenever and wherever I want it to be. There are limitations. Thus we have a huge history of jurisprudence surrounding the whole notion that the 4th only applies when you have a "reasonable expectation of privacy". And when you provide information to a third party to store for your convenience, not pay them for anything for the service (thus you can't really be called a "tenant"), and you allow that third party to read your information so that they can sell better targeted advertisements, you no longer have a reasonable expectation of privacy.
The sad reality of our online world is that the vast majority of our communications now involve 3rd party intermediaries who provide their services for free and when you use those services, your 4th amendment rights don't apply.
Don't like it? Host your own mail server in your house. Encrypt your communications. Use peer to peer encrypted services that don't involve 3rd parties. Avoid communicating with those that use 3rd party services.
Too much trouble for you? Then lobby for some tougher privacy laws or an amendment to the constitution guaranteeing a more absolute right to privacy when you store your information with a 3rd party.