As I understand it the Old West guns were pretty much crap in terms of accuracy, and certainly nothing compared to modern handguns including revolvers.
I think I once saw a Mythbusters segment on this very thing, too.
There is an entire sport devoted to "cowboy action" shooting. I've seen people shoot a hole in a target and chase multiple shots through the same hole, using the weapon's original fixed sights. A single action cartridge revolver can be tuned to be as accurate as any modern counterpart.
Not saying that anyone actually took time to do that back then, but it is possible.