Yes. If you want to know about independent research, a good place to start looking is PubMed. If you do, you'll find this: The influence of elliptical chainrings on 10 km cycling time trial performance, which is a comparison of Rotor Q rings at two different orientations (100 and 110 deg) against round conventional cranks. The riders were "blinded" to the cranks (the cranks were housed in a guard or shroud so the riders couldn't see which ones they were using). The experimental design was randomly counterbalanced. The result was that no statistically significant difference was detected in power or RPE (rating of perceived exertion) between the Q rings and the round ring. Heart rate was higher to a statistically significant degree with the Q rings. The "4%" improvement in power was not observed.
As an aside, if you are testing round vs. eccentric chainrings, you must account for the difference in cadence within the pedal stroke for eccentric rings. This means, for example, that you should either test power differences with a Power Tap or on a rear wheel driven ergometer -- crank-based power meters assume that cadence is constant within each pedal stroke so they can simplify power calculations. If crank angular velocity does vary within the stroke (and high force corresponds with the lower velocity) the estimated power will be biased high. The degree of bias will depend, of course, on the individual rider's exact mix of angular velocity and force application but 3% bias is not unexpected.