A US helmet is actually two helmets worn together. The outer helmet is a steel shell with a mounted chinstrap. The inner helmet fits snugly inside the outer shell and is made of fiberglass and contains the liner straps. The helmet cover is put on over the steel shell and then the rest is tucking into the helmet and the liner is inserted to hold the cover in place. The guys with flaps in the back just didn't tuck their cover in along the back, so the excess would hang down and keep the sun off their necks. Its the same helmet cover everyone else has, its just worn in a non-regulation manner.

It looks like they adopted the Japanese practice of using flaps behind their helmets. Maybe to cover the back of the neck from sun exposure, maybe to drive off the flies on those long jungle marches.