If I rent my house to you, you have unregulated and unrestricted access to it. That does not mean that the government can, without either of us giving permission, search that house.
If you rent your house to me, you no longer have unregulated and unrestricted access to it. You can only access it in certain circumstances defined by landlord-tenant law. That's what creates the expectation of privacy: you know your landlord will only enter your unit for emergencies or with adequate notice to you. You can sue them if they violate these requirements.
The difference with cloud hosting is that, unlike your landlord, your cloud host does have unregulated and unrestricted access to your cloud storage.
In the analogy the customer is the landlord giving access to the could service. Giving someone access to your property does not automatically give the government the right to search it.
Obviously Google is the landlord, since it owns the servers and you're just renting space on them to put your property.
In any case, your analogy doesn't work either way you phrase it. If you're the landlord, and Google is the tenant, then the government doesn't need your permission to access the property, just Google's. The government can't break in and search the servers, but it can get the documents with a valid subpoena duces tecum (subpoena for documents).
> Giving someone access to your property does not automatically give the government the right to search it.
No, but giving potentially hundreds of people you don't know and have never met access to your property does undercut any argument that you have an objectively reasonable expectation of privacy with regards to that property.
Apparently it is not the most intuitive analogy, but it is an example of one party giving custody of their property to someone else. A landlord gives custody of their house to a tenant, a customer gives custody of their email to Google. It seems reasonable that Google could give the government permission to search the email just as a tenant can give the police permission to search a house, but that is not what we are talking about. We are talking about the the government's right to access those emails without Google's permission.
"On Thursday Microsoft will oppose the U.S. government at a hearing in federal court in New York, arguing that it can't force American tech companies to turn over customer emails..."
