I think the TSG can make up pretty much whatever rank they want to. Happy that Jay gets to be a 'pirate' for as long as he wants. Good man, loves the Aggie Band.
Maybe ~15 years ago some satrap at State HQ decided to make the outgoing 49AD CG a 'brevet LTG'; guy wore those 3 stars a few times when he showed up for parties and stuff. No money/pay changed hands. Name doesn't matter but I thought it all rather silly. Man, just retire and let the next guy do his job. Drama queen.
This is not meant to be critical of Jay's deal at all but just something I remember about how semi military/political folks can do what they want, when they want to.