I don't keep track of late night shows like I used to, but still set the recorder and ffwd to the music guests quite often.  Don't have any hard data, but don't think I've ever seen anyone do the same song on a return appearance to a show. 
Plus it would seem like the perfect time to showcase another song from the album. 

Medicine seemed like it was being set up to be the first single, but then Tiny Light went first, followed by Paris, so maybe it is Medicine's turn. 
Personally I'm with Snowbird.  I would love for it to be Oasis, for the reason she gave and because it has a more unique sound. 
But Medicine does have a great hook . . . 
Ain't speculating fun ?  :D