Think about how often Disney uses outside music as a storytelling shorthand for establishing setting or mood. Period accurate music on Sunset Blvd or Main Street. Or culturally relevant melodies and instruments in World Showcase and Animal Kingdom.
Would Impressions de France be the same if instead of French classical music they used that Maurice Chevalier record of him singing Disney songs? Probably not.
There's no substitute for the real thing. Country Bear Jamboree (and Vacation hoedown) uses actual country songs, which gives authenticity to the fantasy. Twangy versions of Disney tunes is not the same, even with the best intentions. There's also the benefit of exposing the next generation to this material, just like the Great Movie Ride. How many people now know "Blood on the Saddle" specifically because of this show? Disney likes to say the parks are not a museum, but showcasing technology, fashion, music, materials and even food from the past are all key components of the Disney theme park experience and the more authentic these elements are, the richer the end result and the more unique each individual offering is.