I concur with you. My firm, 500 strong, has a policy about mailbox limit size. It seems that twice a month the IT dept would let me know that I must do the PST file thing to remove the emails from the server. Until I did this, my incoming email box was blocked. As for the rest of your post, I cannot speculate, however, it seems plausible.
At my most recent work, the organization also has a mailbox limited size and would block the ability to send/receive should that limit be exceeded. HOWEVER, FOR SENIOR EXECUTIVES (Lois Lerner’s position) the limit was HUGE.
If approaching the max allowed size for the mailbox, large files/records could be easily moved to PST files set up for that purpose. Both the mailbox and the PST files WERE HOUSED ON SERVERS. Working copies could have been kept on the individual’s hard drives also for efficiency.