Persistence hunting and the Concorde fallacy

I read about persistence hunting a few months ago:

humans likely practiced persistence hunting, chasing a game animal during the heat of the day, making it run faster than it could maintain, tracking and flushing it if it tried to rest, and repeating the process until the animal literally overheated and collapsed.

And while jogging this morning I wondered if persistence hunting could be the reason why only humans are subject to the Concorde fallacy. A persistence hunter might feel like giving up, but evolution would favour those that didn't. This trait may lead to the Concorde fallacy in other areas of life.