Hmm, that's a good point. I'm aware vaguely of theorems that say what I want but I don't have any references or descriptions off hand. It may just be that one is assuming somewhat low N, but that would be in this sort of context not helpful. I do seem to remember that some version of my statement is true if the variables match bell curves, but I'm not able at the moment to construct or find a precise statement. Consider the claim withdrawn until I've had more time to look into the matter.