Moreover, as a probabilistic matter if one as three variables with two pairs correlated, it is much more likely that the remaining pair will be correlated than anti-correlated, assuming that variables don't have too pathological a distribution.

Where you you get that? The intended probability space isn't clear, but if I take three random directions in N-dimensional space for large N, I find that the chance of two pairs having an angle less than pi/2 and the third an angle greater than pi/2 is about 1.4 times the chance of all three being less than pi/2. The ratio rises to about 3 if I add the requirement that the corresponding correlations are in the range +/- 0.8 (the upper liit of correlations generally found in psychology).