There are two different types of "receives a lot of email". The first type makes up the bulk of the people who receive a lot of email, and that's the type where almost all of the email isn't actionable. Newsletters, receipts, spam, etc. Anything sent in bulk.

The second type is people who receive a lot of correspondence – people expecting a response, or otherwise need action.

The people who claim that it is the receiver's responsibility to process all of their email almost exclusively fall in to the first type, because nobody who falls in to the second type can reasonably process it all.