I'm no expert, in fact I've been asking people on here a few things about dry fasting recently.
but I have done some short dry fasts, about 56 hours was my longest and after that I can say I could understand why people say it is 3x better than water fasting.
I have a problem in my hip where the sciatic nerve has been crushed by the muscle, at one point it was very bad and would not heal at all really.
Water fasting was the only thing that really helped it and it was getting a lot better but was still an unpleasant problem.
After that dry fast it does seem , well, 3x better. The problem has nearly almost completely gone away, ie. the nerve has healed itself.
Also my other hip seems to have healed or something, I didn't know their was anything wrong with it but it feels completely different, like years of wear-and-tear have been healed!
Whenever I fast now the goal will be to only drink when really necessary, ie.real thirst (dry mouth, etc) and if that means going dry for the first 2-3 days then fine.
My advice is to take it easy and gradually go for longer and longer without water but always drink a little when your mouth goes dry.
The last time I did it I only lasted 53 hours and I woke up dreaming of sipping a herbal tea - and my mouth was dry - a good indication your body is telling you it really does need water !!