I think we are missing something here in talking of running buffalo. They did not care if the buffalo ran 3/4 mile after it was shot. What someone would do today is not relevant to the 1840s.
Fredrick Selous (1870s Africa) relates several times wounding Eland and other animals and then driving the animal toward camp sometimes several miles before killing it at a point that was more convenient.
While we are once again at the mercy of the writer Parkman relates that Henry C. his guide killed 2 buffalo at 175 yards with 2 shots using his and Parkman's rifle. The animals ran off and Parkman had thought he missed until they rode on a ways and found the dead animals.
Considering that buffalo that have been hunted often don't let people get very close to them the yardage sounds real enough to me. 175 yards is not far where I live. Buffalo have a large kill zone 3 times what the rifle will likely shoot at 175. I say doable.
Lots of people killed buff with pistols when running them. Colt Dragoons were used for this as I recall. If you had a pistol and it did not kill the buff you put in more powder.
75 yards? This is not as outrageous as some might think. But not knowing the pistol used or how it was loaded we are in the dark to some extent. A fairly long barrel 8-9" and a heavy charge can make pretty good MV. Easily equal to a rifle at 100 yards, about 1000 fps. So now we take the rifle killing at 175 and take the MV of the pistol and then move out 75 yards. We have the same power at the target. So its doable velocity wise. Shooting from a running horse at 75 things get sticky?
I will have to read it again its been years since I read it last.
My question is why would he bother to lie?
He was there, we were not. If the shot is patently impossible then we can doubt. But if its doable then we must accept it as stated.
Its like the story Elmer Keith told of killing a Mule Deer at 400+ yards with his 44 mag. People scoffed. In testing 15 or so years ago I proved that it was perfectly doable with a friends 5" 44 mag.
Elmer finally wrote a book called "Hell I was There" because he was and the people who could not do what he could were not. Lots of people do things routinely that others think are impossible. About 30 years ago dad killed 2 Bull elk about 30 miles south of here a year or so apart. The close one was 400 yards (an intentional head shot at that, first and second shot missed the brain first just under eyes, the second out a little further out and the third broke the neck behind the ear and the elk was MOVING) and the other was 500 plus one shot kill bullet penetrated the heart. Iron sighted 742 Remington in 30-06. Could anyone reading this make these shots? He never doubted he could he just did it.
But at 82 his vision is still better than 20-20.
Dan