Well, I got back to the boat and took some pictures of the hand rail mounting. They actually left me more puzzled than before as to what the PO x 2 actually did when he replaced them.
The first thing you'll notice, is that the screws are located outside of the area covered by the vinyl-over-masonite headliner. In my case, the PO x 2 appears to have used bolts that were too long and actually extend through the fiberglass cabin roof liner. Near as I can tell, he pre-drilled (and splintered) the holes from the inside. The reason I say this is that in most of the (oversize) holes are off-center, and in one of them the bolt actually misses the hole and is pressing against the fiberglass liner from the inside!
All of the bolts appear to have some kind of hard foam or epoxy oozing out around them. Don't know if this was an attempt to seal them, or what's actually holding them in! At least they're all solid and none of them leak.