I was an ordinary helpdesk drone and I had access to all of my customers e-mails. I worked for a large UK DSL ISP.
Infact, I would semi-regularly have customers phoning me up asking me to read out their e-mails, as if I was some sort of human "speaking clock".
"Do I have any e-mails from 'sonnyjim'? Oh, could you read it out to me? See, I'm not at my computer and sonnyjim is my son who's in Australia..."
I would do so if I was happy with the customers identity.
I don't recall anyone ever abusing this facility. From what I saw, the contents of every mailbox I went into wouldn't make riveting reading - it's not all "carry on" affairs in there. We had better things to do, like browsing BBC news and reading Slashdot.