There are lots of references to the shooting accuracy and confidence of American riflemen at about the time of the Revolution. This one by the well known British officer, George Hanger, is much more of a first hand report than the those about T. Murphy because it is based on Hanger's personal experience. Hanger was very interested in arms and shooting and later wrote a book as a guide to sportsmen.
Other eyewitness accounts describe the shooting exhibitions put on by the Virginia and Maryland riflemen on their march to join the Army in Boston at the start of the Rev War. Those involve men being so confident in their fellow frontier riflemen's skills that they shot boards out from between each others' knees --- much to the amazement of the Pennsylvania townfolk. Those accounts have been quoted/published many times and may also be on line if you search Daniel Morgan's riflemen.
Gary
QUOTE from Col. George Hanger
I never in my life saw better rifles (or men who shot better) than those made in America; they are chiefly made in Lancaster, and two or three neighboring towns in that vicinity, in Pennsylvania. The barrels weigh about six pounds two or three ounces, and carry a ball no larger than thirty-six to the pound; at least I never saw one of the larger caliber, and I have seen many hundreds and hundreds. I am not going to relate anything respecting the American war; but to mention one instance, as a proof of most excellent skill of an American rifleman. If any man shew me an instance of better shooting, I will stand corrected.
Colonel, now General Tartleton, and myself, were standing a few yards out of a wood, observing the situation of a part of the enemy which we intended to attack. There was a rivulet in the enemy's front, and a mill on it, to which we stood directly with our horses' heads fronting, observing their motions. It was an absolute plain field between us and the mill; not so much as a single bush on it. Our orderly-bugle stood behind us, about 3 yards, but with his horse's side to our horses' tails. A rifleman passed over the mill-dam, evidently observing two officers, and laid himself down on his belly; for, in such positions, they always lie, to take a good shot at a long distance. He took a deliberate and cool shot at my friend, at me, and the bugle-horn man. (I have passed several times over this ground, and ever observed it with the greatest attention; and I can positively assert that the distance he fired from, at us, was full four hundred yards.)
Now, observe how well this fellow shot. It was in the month of August, and not a breath of wind was stirring. Colonel Tartleton's horse and mine, I am certain, were not anything like two feet apart; for we were in close consultation, how we should attack with our troops, which laid 300 yards in the wood, and could not be perceived by the enemy. A rifle-ball passed between him and me; looking directly to the mill, I observed the flash of the powder. I said to my friend, "I think we had better move, or we shall have two or three of these gentlemen, shortly, amusing themselves at our expence. The words were hardly out of my mouth, when the bugle horn man, behind us, and directly central, jumped off his horse, and said, "Sir, my horse is shot." The horse staggered, fell down, and died. He was shot directly behind the foreleg, near to the heart, at least where the great blood-vessels lie, which lead to the heart. He took the saddle and bridle off, went into the woods, and got another horse. We had a number of spare horses, led by negro lads.