The eigenhead experiment tells us nothing. Not just nothing about human nature, but nothing about anything. According to legitimate, procedurally valid experiments, physical attractiveness is based mostly on symmetry, not on any one physical trait. I'd bet anything the fake face was perfectly symmetric, and with no extreme features (by the nature of averages) to counteract that, perfectly attractive.
The experiment could be made scientific by modifying the averaged head to be only as close to perfect symmetry as the average of the real heads, or by modifying the real ones so they were perfectly symmetric.