Well, that’s an example of good conservationism.
Conservation practices usually involve limiting the number of animals that can be killed during a season, limiting the number of hunting licenses for a specific species, and preventing the killing of young animals and females of reproductive age. All these efforts involve limiting the number of animals hunted.
However, unlimited fishing of wild fish stocks off the east coast has led to the collapse of cod, shrimp and haddock fisheries from Newfoundland to Cape Cod. The collapse of the Canadian cod fisheries is especially well-documented. More cod fishing didn't lead to the cod having more young; it just led to their near-extinction.
The original statement was: The more they are hunted, the more progeny they produce.
For this statement to be true, it would mean that there is some kind of causality between the amount of hunting in a species and the number of young they have.
There is no no proof that the hunting of a species will cause that species to produce more children as a result. There is no causality between the two whatsoever, from everything in biology that I have ever studied. I wondered if there was any evidence behind "I just think that it's so." Apparently not.