When the "rules" were violated in the Waxhaws, etc., the Brits (specifically Tarleton and Wemyss) ratcheted up the reprisals/outrages, and thus lost the Carolinas. Then they lost the thirteen colonies.
COMPLETELY, totally, absolutely, 100% false.
One of the worst and hardest to kill myths of the American Revolution.
The primary mode of fighting in the Revolution was the Continental Army fighting in lines in open fields PRECISELY as the British did. Von Steuben was brought in to train our troops in pretty much precisely the same drills and tactics as the British.
Linear tactics WORKED in populated areas with a halfway decent road network with a good deal of open space, such as much of the colonies in the Revolution. They helped discpline and were often the only way to get good firepower with a horribly inaccurate and short-range musket. There was nothing stupid about them.
In the South, most of the war was in fact a Civil War with most of the fighting between guerilla bands of rebels and loyalists, with some fighting between regulars towards the end of the war.
There was guerilla-type sniping by the US at Concord at the very beginning of the war.
But other than that, the overwhelming majority of the fighting was either European-style linear battles, or sieges. Bunker hill was the British attacking an entrenched position, not an ambush. The Continental Army fought its battles with linear tactics (and it really shocked the British when the Continental Army was able to go toe-to-toe with them in an European style linear field battle at Monmouth...which we almost won but ended up as a draw.
In fact, MOST of the "backwoods ambushes" in the Revolution were British and Indian troops ambushing AMERICAN troops.
"The Rules" were not to march in lines. That was a simple matter of effectiveness with the weapons at hand. We really didn't do all that well with skirmishers in most places, as they weren't well trained for that. In any case, the British had skirmish unit too, and darn good ones.
As for the main point, yes, by and large Continental troops DID play by the rules. It was insisted upon, because where they didn't no quarter was given.