The BB in question asked if I (as the owner, not as an admin) could read PM's. My instinct was to respond, "of course not!" but I thought about it for a moment....while I've had admin/moderator rights on phpBB boards before, I've never actually hosted one on my own webspace. I thought I'd better check more closely before answering. So, I did.
PM's, unlike passwords, are not encrypted. I can't see who wrote what, but I can read them.

I considered keeping this information to myself for about 0.000000013 seconds, but then decided that everyone should know. All of you are placing a certain level of trust in me by residing in a place that I have control over, and I take that very seriously. I can't imagine many scenarios in which I would find it necessary to look at the PM's in the database (I get sued and someone subpoenas the database? Someone breaks in to my apartment, holds me at gunpoint, and tells me I have to look?) I'll go on the record now and say that I have no intention of ever looking at them, period.
I hope everyone who wants to will still choose to utilize the PM feature on this site, but only if you feel comfortable doing so.
So, there you are. Don't hesitate to post your questions and concerns or PM me.
