I think it has more to do with the type of slings they use now. The M1 sling was basically a carry over the shoulder device and the M16 sling allows to keep the rifle at the ready-low position.
The M16 sling was the same as the M1 sling. Only fairly recently, particularly with the M4, has it changed to a low-ready carry (easily). When I was in Basic Training, back in 1998, we used M16s, but had to carry them at the low-ready anyway. That light rifle got to be a rather heavy brick after 12 or so miles of humping.
The new sling setup for the M4 is MUCH better.
Oh, and the scene where being referenced here is lame. No Infantry squad would walk through enemy territory in a wedge formation and carry on a conversation. Hollywood nonsense, but it had to service the plot.