This doesn't really answer your question...
While we weren't guided while we were there, my impression is that you'd be equally served to sleep in Mulas like (nearly) everyone else. Indeed, folks were sleeping and showering at the Refugio, but frankly, what's the point? I assume there might be a tad less noise and the beds might be a bit softer...but maybe not. Other than the Internet and phones, the place was a touch on the primitive side.
Whatever suits you, man. Refugio is only a 15-20 minute walk from Mulas.