This post by Ubisoft lists him as a Master Sergeant, which isn't a rank in the Navy. The equivalent in the SEALs would have been senior chief special warfare operator.
So he's not on loan, he's been transferred to the Army.
This.Originally Posted by nyleken Go to original post
Also as Ghost Recon are modelled after SFOD-D, "Delta Force", it is reasonable to understand them to be a unit that recruits from across JSOC but is 100% a US Army unit.
Karen Bowman on the other hand, despite using the callsign "Ghost Actual", is not a member of the unit, she is just their CIA commander.