there's not really enough Borodin in the score IMO
I'm sure you're right. I don't know the Borodin sources well enough to say.
Check this out:
Robert Wright and George Forrest had adapted classical music for shows and pop songs before (Grieg for Song of Norway and Rimsky-Korsakov for the film Balalaika), but Borodin was actually their third choice for Kismet. And, fortunately for them, by the time they finished writing, Borodin’s music had come into the public domain so they wouldn’t have to pay royalties. As it turned out, they filed their copyright on Kismet the very day that the copyright on Borodin’s music expired.