If you're going somewhere like Bonaire, you can shore dive without someone staying on the boat (er, shore). The shore isn't going anywhere. A boat, on the other hand, *could* end up going somewhere, and floating along next to each other in the middle of open water makes for a rather un-honeymoon-y afternoon, evening, night, following day, etc.
Sure, it's probably a decently good idea to dive with someone who knows the area, or at the very least, talk to people who know the area well. The unattended boat concept, on the other hand, makes me a bit too apprehensive. (I'll dive off a small boat or canoe in a lake, as I can handle a mile or two of leisurely finning, but open water? Oi!)
(Incidentally, when we were rank newbies fresh out of class, my significant buddy and I took a trip by ourselves to do several spring and shore dives. We were extra careful, but we didn't bring anyone else along. Her parents, on the other hand, would have me quite worried if they went off without someone to guide them.)