OK, I do see messages like: bayes: cannot open bayes databases /net/mail/etc/mail/spamassassin/site-wide/bayes_* R/W: lock failed: File exists
I moved to a site-wide database because most users aren't going to bother with training, so I figured this way all users can benefit from the training that a few users do. But it does seem to be a problem that only one user can access the DB at the same time.