That's made for a bolt on receiver, rather than a hitch ball. Exactly as you say, it's a class III receiver frame just without the "receiver" portion. If I remember correctly the top of the hole in the bumper is convex to match the bolt which has a concave head.. The bolt that goes through the bumper is really long and most balls wouldn't have nearly a long enough shaft to get through.

There's tons of aftermarket versions, here's an example.

https://www.amazon.com/CURT-13333-Class-Trailer-Hitch/dp/B002GO784Y