Billy Dixon always noted that his shot at Adobe Walls was a "scratch shot", meaning it was just a fortunate shot at that range. Notwithstanding both the Sharps and Remington Rolling Block were accurate rifles, within reason. Yes if shooters set up their rifle for specific long range shots to replicate the Dixon scratch shot, it is possible to duplicate it. It is though as Elmer Keith stated that he could "work up" a target too with a pistol to astound people he was guiding. Again by this, Elmer would lay on his back, put the pistol, usually a Colt 45, next to his calf for steadying the shot, and shoot at targets at incredible distances. He simply would "walk" the bullet onto the target in five or six shot at incredible distances.
That stated, a 22 rimfire is lethal to a mile, and if you elevated correctly for that distance, you would get on a target. Carlos Hathcock the noted Marine Sniper provided a formula for shooting long distance, factoring in wind, temperature in watching the mirage angle and humidity ar all factors in hitting a target.
With the buffalo rifles, they were firing large lumps of lead, which carry more true than lighter calibers. Most Americans, fired a paper patch or an antelope skin bullet. They used American powders, which are produced with different charcoal compared to British powders. The American powders burned drier than the British, so did not produce the power the British powders did. This was explained by Frank Meyer in his book. He always fired British powders which were more expensive, but his rifle was a 40 90 Sharps, and he was able with that powder, a heavier bullet than most 40's were loaded for to actually match the 45 120.
Buffalo Bill shot a 50 70 Springfield, and he did remarkable shooting at reasonable distances. General Custer had a 50 70 Remington and was very fond of that rifle too. All military cartridges were 50 70 in that period. This was what was offered to adventurers in free ammo to kill buffalo as a public policy to bring Indian rampages to an end, as it was deemed more humane than killing off the Indians in war. This is where the genesis of the 50's originated in civilian rifles. The calibers which were available were 44 in Remington, to the 45 to 50. Lengths extended for powder charges, and telescopic sites improved distance shooting. Bottleneck cartridges started appearing in this era, but the fouled barrels caused these cartridges to stick sometimes. It is why most favored the straight wall.
There is a really good article on the Big 50 in the American Rifleman. I will provide the link, but in it you will find the 50 was not quite generic. Frank Meyer or Mayer stated that anyone could order a rifle in any configuration they dreamed up. The "experts" in the old Buff Runners knew of the types of rifles they had, but one 50 actually had over a three inch cartridge and fired a 700 grain bullet. It is akin to why modern snipers are hitting targets with the 50 BMG, Browning Machine Gun rounds.
Hope the additional information helps.
Big 50