Are those located just above Vernal Fall or at the footbridge where the Mist and John Muir trails separate?
I remember seeing composting toilets in the comfort station above Vernal Fall. I don't remember a water fountain there, but I wasn't looking for one.
The toilets near the footbridge are flushies, so they'd need water to operate. There is a drinking fountain there (with faucets for filling bottles). I tried the water last July, and wished I'd filtered it first. It seemed to have obscene amounts of chlorine (or chloramine) in it.