I'm not sure how common it is, and it's probably less so now with email, but I'd guess a lot of important people do have their assistants screen their confidential mail. For example, I know politicians often have people help with their mail.
A new cleaning company called CleanU create an app where people can easy order office cleaning by a single press of a button. In the ToS/service/liability contract on page 43, it says in legalize: "any document found by our assistants might be used to improve service and decrease costs".
This might sound as a great way to start a legit industry espionage service, but alas, it would be illegal under several laws. First, a judge would ask if there had been a merging of minds, and thus declare the contract void since no buyer could possible have agreed to such terms. Second, as a product (sale), one could ask if "theft" could reasonable be expected when one purchase cleaning. Since it can't, the contract can be made void in that way. Thirdly, if the intent is to hide an otherwise illegal activity under the assumption that people do not read EULA, that would qualify criminal charges under Mens rea, thus fraud.
In all, reading peoples mail because you managed to get people to click a box during registration is a deal on a very unstable legal ground. Law suits like this will explore exactly how unstable it is.
Cleaning services are also reasonably expected to clean desks. They might even temporary hold confidential documents in their hands while doing so. However, once they start reading the document and interpret them, a line has been crossed which no legal fine print can fix.
Many people sign NDA's. If you have an assistant read mails covered by the NDA, then the party who sent the mail can sue.
and so on and so on.