We're not seizing the high ground as we don't have enough troops and we don't have enough helos to move them. The Sovs just about managed to hold their own prior to Stinger with 100 to 150 thousand troops but they still used to lose more helos in some missions than the UK has in theatre.
As to cover, I read those engagements as the US using HMMVW and MRAP with 40mm grenade, 7.62 and 12.7, and dismounted with M4 or whatever plus loads of gucci add-ons. The Soviets used tanks, BMP, BTR as platforms, equipping their dismounted troops with "man portable" 82mm mortars (Podnos), manpack 12.7 (NSV), manpack 30mm AGL (Flamya) and RPG. In other words, the Red Army decades ago outgunned todays US troops.
And yes, I also read the subtext as "without CAS, we would be dead".
Did you also notice how slide 5 comes straight out of "The Bear came over the Mountain" ? The locals did all this to the Red Army, now they're doing the same to us. No conspiracy theories about training are needed.
And on that subject, if you haven't got a copy of that book and the companion "The Other Side of the Mountain" from the US Foreign Military Studies Office yet (free to allies, ie us) then you're not prepared for Herrick.