I didn't see where he's doing a concours restoration, but if that's the case you're probably right. If not, I don't think you'd notice a difference unless viewing them side by side, and when's that gonna happen? The vinyl is extremely close to the originals (see the photos) and is much more durable than painting. Plus, any imperfections (scratches, etc.) won't be seen in the new vinyl so, unless you're doing a 100 point-resto, I think you'd be overall happier having them re-finished. I know I get A LOT of compliments on mine.
Mike