Yes, it does rotate.
However, the vast majority of those ships are contracted container and roll-on/roll-off vessels that are directly controlled by the requesting authority. When it comes to land-based material assets, the bulk of these ships and sorties are Army controlled.
But, it's only a hook.
The Army doesn't really have a Navy ;)
When they let us put guns on board those ships, THEN we'll have a Navy.
Please, I'm a boat driver, If you guys get to put guns on your cargo ships then we have to start crawling around in the mud. Want an ugly picture? Sailors marching! That's why the Navy has the Marines, so sailors don't have to march.