This is pretty much standard practice for Jeep and 4x4 offriding, whether rock or sand. 15PSI is fine for pretty much any tire. The lower pressure not only gives a better ride, but the tire will grip the rocks much better. In sand, it disperses the weight over a wider surface and you won't sink into the sand as easily.
I was at the beach once with my Jeep, with my buddy following in his Ram Truck 4x4. I suggested he lower his air pressure (He liked to run at 80PSI) and he poopooed the idea. He made it about 50 yards before he sank to his frame. Two little old ladies, about 75 years old, rolled up in their little Suzuki 4x4, took one look, and said, "You should have aired down". Needless to say, we still laugh about that one. We aired him down, I used the jeep to pull him out of his holes, and he did fine after that.
Yes, air down. However, don't run any longer than you have to once back on the highway. You will overheat the tires and cause damage. Just take it easy and go slow til you can refill.
2005 Coachmen Sportscoach Encore 380DS
2019 Jeep Wrangler Rubicon Unlimited