Reverse-engineering from the article, the original statistical result was probably something like, "Variations among managers in technical skill account for very little of the variations among managers in performance reviews."

One way to get that result would be for technical skill to be unimportant. Another way would be for the variations in technical skill within the sample to be much smaller than other relevant variations. Given that (según the article) the managers were selected for technical skill, but not for the other qualities, it seems almost certain that this was the case.

This might sound like a bug that could be avoided by better statistical analysis techniques, but it's really not. You really want to know what causes the actual variations in performance in your sample, not what could conceivably cause variations in performance. Surely there are hundreds of things that would cause even bigger variations than what's in your actual sample — you could have managers who kill all their employees, or managers who are interned incommunicado in Guantanamo, or managers who obsessively turn every project into an investigation of fluoride contamination of their precious bodily fluids, or managers who are actually undercover headhunters from a competitor trying to steal away all of your best talent.

Cosma Shalizi has an excellent post about the pitfalls of multivariate statistical analysis at http://www.cscs.umich.edu/~crshalizi/weblog/520.html; although he's talking about genetics, it's very likely that what he's saying applies to Project Oxygen as well:

To see why gene-environment interactions matter, consider one of the best-established links between genetic variations and intelligence, phenylketonuria. This is a recessive genetic disease which interferes with the normal metabolism of the amino acid phenylalanine. If someone with one of the defective forms of the gene for phenylalanine hydroxylase consumes too much dietary phenylalanine, it leads, among other problems, to serious mental retardation. Under suitable diets low in phenylalanine, however, they grow up mentally normal. Assigning shares of this effect to the genes and to the environment is exactly as sensible as trying to say how much of the fact that a car can go is due to its having an engine and how much is due to their being fuel in the tank. The best the usual biometric model could do here would be to predict that having the gene always reduced intelligence, as did consuming phenylalanine (which would be bad news for makers of artificial sweeteners); the fact that it's the combination, and only the combination, which is a problem would be missed, and the predicted size of the effect would be badly wrong. … So while everyone piously says that genes and environments interact in development, they typically use models which assume that they do so only in trivial ways, and hope that any actual interactions are small enough to be treated as noise.

(So if these simple linear models are so bad, why does everybody use them? Because they have fewer parameters than more complicated models, which means that they're not as prone to overfitting. It's easy to construct a nonlinear multivariate statistical model with more parameters than you have managers in your company, which will discover correlations no more meaningful than the fact that people whose initials are "BHO" are far more likely to currently be the president of the United States than people with other sets of initials.)