I guess that depends on what you consider to be logistical independence, but at the theater scale, the answer is "no". Physically moving personnel and materiel to Africa, say, is almost always handled by the U.S. Air Force to a very large degree. See for example, Operation Serval.
Could you unpack that? I don’t know what you mean, but it sounds interesting.
My MOS was a 2844, which was a Ground Radio Technician. I could repair and operate every radio the USMC had at an advanced level. I then received courses on how to provide EMT-level care on the battlefield, machine gunners school, vehicle operations (command, gunning, operation, egress, maneuvers), basic generator troubleshooting, vehicle maintenance training, artillery/medevac coordination, advanced SatComm training, etc... This is specifically so that teams are a) self-sustaining (one team can accomplish many jobs outside of their primary job) and b) to reduce the number of on-hand resources the USMC requires to function.
What you're describing is taught to us as the difference between an occupying force and an expeditionary force. Occupying forces don't really need to be trained on seizing forward air bases because someone else does that. That kind of army functions a lot more like well-armed police. The Marines has a different decree, which holds most units at a high level of unit readiness because the president has the capacity to deploy them for 30 days at any given time. We operated most battlefield functions as internal jobs, aside from ships logistics, and cross-training is heavily emphasized to combat cost. Interestingly enough, the Marines is the smallest and least funded branch in the armed forces - so it would appear the difference is primarily in culture, logistics, and tactics.
Edit:
All this said, we operated and trained with British, Korean, Aussie, and Dutch military components that had and trained on these capabilities.