*whispers* no they didn't
Ah, yeah, they did. 
That was back in the 1960s and 1970s during the Nam. The SKS rifle was especially prized among the US grunts as trophies. Some kept them because the M-16 was a real POS back then. Jam City. Probably a lot better these days though, nobody hears complaints about them anymore.
As trophies, yes. As a weapon, soldiers would pick up the AKs that were just as common that fired the same round full auto with a larger capacity, detachable magazine.
And yeah, the AR-15 became perfectly reliable starting with the XM16E1 (later made into the M16A1), as well as the issuance of cleaning kits and instructions and the use of cleaner-burning gunpowder.
Despite the reputation of the two weapons, the AK-47 isn't mythological and the M16 isn't a piece of crap. The AK is more durable and reliable, but it'll still malfunction or break if you don't take care of it; it'll just last longer than some competitors. The M16 requires more regular cleaning, but it'll function flawlessly if kept maintained and the requirements aren't so stringent that a soldier would be incapable of performing them. For civilians, you have no excuse for not cleaning it.
