I think leather was used a lot for patching material around the world in less developed areas for hundreds of years. But we are talking about early America here.
Why is it so hard to believe animal hides were used, and quite often, for patching?
Cloth was often in short supply, and expensive; so much so that being a rag merchant was a common occupation.
In some locales,getting decent fabric, let alone proper thickness, would have been impossible.
Animal skins, on the other hand, could usually be obtained easily, be they deer, squirrels, raccoons, badgers, groundhogs, etc.
Having used leather patching myself, I can say that while it has not always given me the very best accuracy, it is at least functional, and often performs very well; certainly good enough for hunting and fighting.
The thing that makes leather in some ways better than fabric is it's compressibility, which makes it more forgiving of ball diameter-it expands to grip a smaller ball well enough, and compresses down equally well when used with a larger ball.
This compressibility also makes the actual thickness of the leather less critical when used with a given barrel and ball combination.
I havn't tried it myself yet, but I would not be surprised that whatever animal hide was used need not even be tanned.
If a person shot a squirrel and skinned it, scraped the hair off, then rubbed your grease or oil of choice into it within a few hours, would this keep the hide pliable enough to be used for patching for a few days?
Hmmmm, idea for an experiment.