No, they couldn't. As the main songwriter, Taylor effectively controls the sync rights and can decide to only offer up versions she controls the master recording rights to. That's the entire point of the Taylor's versions. She can't prevent the originals from being played on the radio etc, but any movie, ad, or other promotion would require her approval and she has denied them for all the originals to date.
And pretty much only Taylor can do this because she wrote or co-wrote her entire discography.