I read a book not too long ago by a German MG34/MG42 LMG gunner. He began as an assistant gunner and then rose to gunner. He served on the eastern front and in the Vosges area. I seem to recall that he might have been SS. Anyway, he was always at platoon level, which, I believe differed from the HMG teams in that the latter were attached at higher levels in the order. He nearly always had an assistant gunner, whether trained or drawn from the platoon. It should be noted that most members of the platoon carried extra mortar rounds or MG ammo belts or cans when fully supplied and moving to a new tactical location (that is, when they had enough extra ammo on hand). When on assault, they carried only their personal weapons and ammo.
As with other armies, he often went out on patrols with a rifle in hand, even though he was considered a specialist. The demands of limited manpower, I suppose. It is interesting to note that every book I have ever read indicates that the German ground forces were always under strength after the war began. Of course, this deficit worsened as the war went on.