Bettas are micropredators (I'm sorry if this term is not exactly accurate, I can really only find this word used in this context within the fishy world, and not as a scientific word for a type of predation). Which means their prey is mostly things they can eat in a bite or two. They generally eat tiny invertebrates; insect larvae, small worms & crustaceans and any small bugs unlucky enough to land on the surface of the water.
In response to the hunter statement, there are many different types of predators, some that hunt and some that don't. For instance one could be an ambush predator, not a hunter. Bettas on the other hand tend to be opportunistic predators (they attack prey that can be approached and eaten with little expenditure of energy).
Also, the idea that worms cause dropsy seems inaccurate, as it is a type of food bettas are used to feeding on. The idea probably comes from the fact that live prey can often leave much waste on the bottom, which in turn degrades water quality and causes dropsy. I cannot imagine that worms themselves cause dropsy, and would be interested to see a source that states that information (and what their basis is).