I think the concern is if the valve is only slightly open. The story I've heard is that the valve will only provide enough gas to breathe at the surface but as soon as you get a few feet and the flow requirement increases it will no longer be able to provide the gas quickly enough. Once you get to a certain depth, which I presume would vary based on how open the valve really was, you wouldn't be able to draw any air from the reg - or very little.
I think most of us - at least it's the case for me - are just regurgitating what instructors have told us. Accurate? I've never tested it personally. I've found a thing or two that instructors have said to me over the years to be incorrect so I'll withhold judgement I guess. I've never tested that whole "bends" thing either.. call me conservative, I guess. Most - probably a good 95% of what any instructor has said to me, is either obvious or I've personally experienced such that I can say I proved it to be true. I do make every effort to ensure my gas is all the way on before I splash and that 1/4 turn back nonsense can be damned.