P.S. The show version of HOW TO SUCCEED does have Rosemary sing one verse of a ballad version of "I Believe in You" as a reprise, late in Act II, so there is that precedent for the way it's done in the movie.
I'm going to be pedantic here, but so be it, lol. She only gets one A section of the refrain - not a whole refrain, and not the verse (which is only sung by Finch - i.e. "Now there you are..." etc). But yes, your point about the precedent is right. ;-)