Robbery may have been the motive, if I recall correctly. The Dineses were out very late at a club in town, and returning to their home around 4 in the morning the guy attacked them just south of town. They fought back -- Alan Dines was recently retired from the British military -- but to no avail.
The island does have crime, a bit more probably than many people would think, but perhaps not more than one would expect in a "well-to-do" town of 10,000 or so located in a region of considerable poverty and which each year gets 75,000 or so "wealthy" international tourists (all things being relative). The island is a natural magnet for n'er do wells from other areas, not just from Belize but from neighboring countries.
I don't know that reliable crime stats exist. The Belize government releases statistics regularly, but they seem to fly in the face of common sense. Plus, naturally, it is in the best interest of hotels and other tourism related interests on Ambergris (which is just about everybody) to avoid publicizing crime, especially crimes involving visitros. That's the case anywhere in the world where visitors are an economic factor.
Actually, though, given the high-crime areas that are nearby -- Belize City for example -- not to mention neighboring Guatemala and Honduras, crime in San Pedro is remarkably low. That's a tribute to the San Pedranos who keep an eye out for the bad eggs who come on the island.
No, I don't live on Ambergris. Maybe some of residents will pipe up. But, again, "the less said about crime tbe better" is the natural and very understandable view of anyone who sells hotel space, real estate, tours, or whatever, to visitors.