I haven't read David Fowler's original article, but to go by Paul Slade's summary combined with his fresh information from the archives, the basic idea seems plausible enough. On the other hand I think Paul Slade also has a point in casting doubt on Fowler's identification of the likely murderer as John Billson. His first argument, that the records show that Billson must have been at least in his 40s and the actions in the ballad seem like those of a much younger man, perhaps involves too many presuppositions about someone we know practically nothing about, but I find the second, that the ballad actually says the murderer was "carpenter's mate", more persuasive. Calling any carpenter working on a ship a "ship carpenter" makes sense, but why bother to identify his position more precisely as "carpenter's mate" if he was actually the master carpenter? (Unless, of course, the writer was deliberately making the murderer younger for the sake of the story.)

The main weakness seems to me to be the failure of either David Fowler or Paul Slade to find record of a burial in Gosport that looks like that of the victim, but I'm sure there are plenty of possible explanations for that.