It was initially intended that the Lebanese army would not enter Palestine at all but just defend the border.  There was a lot of opposition in Lebanon to getting involved in the war.  In the end, they had some small involvement.  The skirmishes inside Lebanon were due to Jewish forces entering Lebanon.  They got as far as the Litani River and some of the Israeli generals wanted to keep going.  Anyway, to get back to the point, I agree that forces in support roles get counted as well as those in combat.  Within limits, naturally.