FG42s are automtic rifles, like the BAR. Actually theyre one of the most advanced weapons of WW2, and had virtually no recoil despite firing the powerful 7.92x57mm cartridge even in fully automatic from the standing posture. An inline stock and quality muzzle brake help with this.
The internals of the gun would go on toninlfuence the M16 and the M60 post-war. It was way ahead of its time for WW2, but very few were made and issued, and of course only to Fallschirmjager units.
Whats wierd is CoH lets you get 4 per squad, but CoH is worse for realism than that in many more ways.
The FG42 was an awesome weapon, way ahead of it's time. It was much better than a BAR being much lighter and more controllable. It makes perfect sense for Fallschrimjagers to be able to fire on the move, in fact it would be dumb not to have it that way.
Are Fallschrimjagers they OP right? Maybe, I haven't faced them yet but I did use them to stomp a USF player the other day. I only built Strums and Kubels until they make available them called in 3 units.