Both victims are women. Interesting.
The men they were with didn't need to run faster than the buffalo, just faster than the women.
If we’ve got to use the word “outran”, This Guy likes your version: Men “outran” the women.
But to finish editing the government’s warning: Bison can outrun humans. But this is only a euphemism. The real point to make is that Bison can “run down” humans In this case they certainly “ran down” the “outrun” women!