Areas outside of the shower just need a good coat of paint. Now, if the stuff is made out of MDF, or some composite, I'd be a little leary using it in a bathroom, but having moisture resistant material behind it would in no way improve its life assuming this isn't an outside wall which should have a vapor barrier there.
So, just make sure you get a good coat of paint on the stuff, and consider painting the back side as well. If you don't have an exhaust fan, consider putting one in and using it to keep the humidity levels down.
If their concern was to trap moisture behind the stuff, a vapor barrier installed over the walls prior to installation of the wainscoating should resolve that.
GP Densshield fiberglass coated drywall doesn't have paper on the surface. Paper acts like mold food if it gets wet. I don't think you need it, but that might make you feel better.