Apparently they had setup their Exchange server poorly and I'd had access to any number of mailboxes (including the CEOs) and other folders that I wasn't supposed to have access to. I was completely unaware of this access, but was being directly accused of having access confidential information.
I insisted, truly, that I wasn't aware of the access and hadn't looked at anything confidential, but they tried to tell me they had proof that I had accessed email I shouldn't have. At this I got upset and demanded they show me this proof, which they couldn't do because they didn't have any, but I'm guessing they thought I had seen some stuff and they could get me to cave it if they pretended they had proof.
Anyways, I didn't get in any real trouble because I wasn't intimidated, but it damaged the relationship and I ended up quitting a few months later. Now I feel the same way as OP, I don't want to be in a position where someone can make a plausible accusation of misconduct, you could be totally honest and still end up railroaded just for being in the wrong place at the wrong time. CYA.