What makes you think the US does not have boots on the ground?
We have contractors and some teams for specific ops like securing their mustard gas, etc. After the drones arrived they weren't needed, the Brits and French have done a passable job.
We have had a number of State Dept. personnel that have security with them.
Our boots and air support would have finished this a long time ago.
We trained the Qatari's and Jordanian Spec Ops teams that are there, so not much difference. I would expect that we have some trainers there.