I decided to break out the textbooks...Black Book and Perl In A Nutshell.

Both of them are very quick when discussing dbmopen and dbmclose, but at the same time...both books say this, "If you don't have write access to the DBM file, you can only read the hash variables, not set them."
Both books barely even discuss the functions, but take time to make that same point. Maybe it was how you opened the DB file, or it may just be your actual privileges on the file itself.
I wish I worked with DBM files so I could provide a guaranteed answer, but permissions may very well be the problem.