Hello,
Brian, your .7071 ratio, is also 50% of the square root of the number 2. Aliens?? I believe that the longer neck to bore ratio, is not an absolute law that dooms those with a short neck to failure, but that the longer neck, with a bullet seated nearly to the bottom, will make "better" accuracy, easier to achieve. If the bullet is seated in the case, and good axial alignment is achieved, we are headed toward success. What happens to a bullet's alignment, from the time of seating, until it is fired, do to outside forces, caused by feeding from a magazine, and transportation of the ammo(point up/point down, boxes dropped, thrown into a bag) are all factors to consider. A longer neck will help to overcome any of these things, that may, or may not happen to your ammo.
The point was made that "acceptable accuracy", should be determined by the individual, based upon his/her application. Absolutely!
The 22PPC, has a neck length of .286", while the 222Rem., has a neck length over .3" I would not consider neck length/bore dia., a myth, as I think that it helps to achieve any level of accuracy. One of the most important pieces to the puzzle, is to use your equipment, often enough to know the trigger, and to control the breathing, and jitters, that are magnified by a scope.
Regards,
Bob