Agree. But it so happens that my head Drill Sgt. made E-6 in the USMC as a DI and instead of re-upping in the Corps went to the Army for reasons unknown, and insisted we called him DI and that's where I get it. He was the only Drill Sargeant in Ft. Dix allowed to wear the gold belt buckle on his field belt. I'm trying to recall his name...yes, SSG Manzanares. Not only did he yell at us a lot but also at the straight-Army DS's under him.
I've heard of Marines transferring to the Army and retaining their rank, but I've never heard of an soldier transferring into the Marines and retaining rank. It may happen, but I've never heard of it.