I'm not sure why you're attempting to call out non-existent fallacies and having so much difficulty accepting the hypothesis.
The person in question averaged roughly 40 miles per day. The specific example provided in the wikipedia article - full of citations to supplementary materials - detail a group running up to 35 miles per day.
So it's not at all like persistence hunting - something done by traveling a long distance, usually running, over an extended period of time - because people are running for too far of a distance or for too long a time?
Wow you're so right; I mean, when's the last time you ran anything more than 5km? That's likely some concrete evidence of humans not being able to persistence hunt. Or is that a non-sequitur, too?
https://physoc.onlinelibrary.wiley.com/doi/10.1113/EP088502