I totally agree that a "stranger" shouldn't ever touch anyone equipment without permission. I have always set up my own equipment prior to diving until recently.
When I was diving in the Keys last year we were diving on a six pack and I had complete confidence in the Captain switching out the tanks. Yes, I took 3 or 4 deep breathes and watched the guage prior to entering the water...just in case.
On my latest trip to Honduras the Captain and DiveMaster both set up equipment before we even arrived at the boat and changed tanks between dives. Again, both of these men were extremely professional and took a great deal of care when changing over the equipment. I never felt the least bit uncomfortable on this trip.
In both of those case the folks changing out my equipment were total strangers. Initially I reviewed what they did and how they did it and felt comfortable with what they were doing.
But would I let just anyone on a boat touch my equipment? Hell no. I have three or 4 people I dive with that I trust enough to set up my equipment...and even then I check it, my buddy checks it and then I can relax.
How about you? Will you let a Captain or DiveMaster change your equipment or is that taboo for you also?