I found an image on Yachtworld.
There is definitely bolts that go from the inside through the fiberglass and into the handrail, much like a t-nut. If you can't see them from inside of the cabinet, then first look up to see if you can see the fasteners for the counter. If so, remove the counter.
If not, then see if the entire storage cabinet is installed. You might need to remove the storage cabinet itself. I mean only the doors and the shelf unit that looks like it slides into the fiberglass bump out.