So I've spent the better part of the afternoon tinkering and experimenting with this.
On Al Rayak, I placed modules for RHS USMC (AI commander, Civ obj, Mil Obj, Mil Logistics). I then placed Player combat logistics..and set it to Side and Faction.
I then placed down a player unit as RHS Socom Operator. I called in Logistics for 2 USMC Squads to land near me. It says the helos were loaded..then it says they were destroyed in transit. I called in Air Drop for the same squads...nothing.
I then switched to a player unit as RHS USMC Soldier. Same thing..called in logistics....RHS Choppers show up, drop off the troops.
I tested this several times. The common theme appears to be that if I play as an RHS Socom Operator I can't call in any logistics at all. If I play as US Army or USMC, logistics works.
Just passing this along.