There's some evidence that humans lost their fur as an adaptation for persistance hunting - our greater heat loss ability allows us to keep going for longer. Clothes, even furs, are not equivalent to having your own fur because you can just take them on and off.
Attributing our {rare} loss of hair to our {unique} long-distance ability in this regard is a logical (causal) fallacy -- they are not necessarily connected.
Who said they are necessarily connected? There's no logical fallacy involved in constructing a hypothesis based on available evidence so long as one understands that it is a hypothesis.
Re: This Whole Reduction of Hair for Running Down Prey Thing
No.
Because the starting point is different. Humans evolved from apes; Hyenas are dogs. Dogs already have a pretty good heat loss system - panting; apes don't. Apes already have good manipulative skills, allowing them to make nests to keep warm at night; dogs don't. Hyena have good night vision and hunt primarily at night; humans and chimps don't.