For the last day or so I've been going through my references, including the U.S. Navy Diving Manual from March 1970, the NOAA Diving Manual from 1975, and my two copies of The New Science of Skin and Scuba Diving, plus several other texts, and I can find no reference to the 1/4 turn back.
However, I always use this practice myself. So I wondered my memory banks, and got out my valves (I have several not on tanks). One is an old USD 3/4 inch valve, that I have partially disassembled in front of me. The stem of this valve, which is what unscrews the seat, has on its top a soft plastic disc that seals the top of the valve. I started diving in 1959, and got certified in 1963 from LA County's instructor, Mr. Roy France. He did teach the 1/4 turn back off full open. And if my memory bank is correct, he had a reason. That soft plastic disc can be scared if the valve is opened "hard." If someone twists that valve open with sufficient force, damage can be done to the top of the valve internally which can lead to a HP leak. Young male types tend to over-do things, and he cautioned to simply open the valve all the way, then back it off 1/4 turn. That way the only pressure on this plastic disc is the air pressure itself and the spring tension from the top of the valve, and not the mechanical advantage that the threads and handle can give against this plastic disc. This technique will lengthen the service life of the valve, because the plastic disc will remain undamaged by the forces of a young (usually guy's) hand on the valve's wheel nut (the thingy you use to open the valve). This plastic disc, on the old USD double-tank valve, is part #26 (U.S. Navy Diving Manual, March 1970). These valves have retained their same basic design since the early days of diving internally. So I think this still applies.
Concerning turning the valve the wrong way, I found on my valves a mixed bag of on-off indicators. Scubapro and Sherwood both had on-off indicated on the valve's wheel. But others, including AMF Voit and USD did not. This is part of what I was showing in the diagram--"Person-Machine Communication" for "Words and Symbols" that can be a factor in an incident/accident. I can go back to what a friend of mine in facility maintenance said. "Lefty-Loosy, Righty-Tighty," said Steve Harris. (Left--counterclockwise; right--clockwise.) I've never forgotten that since he said it.
SeaRat