It has recently been suggested that the presence of multiple populations showing various amounts of helium enhancement is the rule, rather than the exception, among globular star clusters. An important prediction of this helium enhancement scenario is that the helium-enhanced blue horizontal branch (HB) stars should be brighter than the red HB stars which are not helium-enhanced. In this Letter, we test this prediction in the case of the Galactic globular cluster M3 (NGC 5272), for which the helium-enhancement scenario predicts helium enhancements of > 0.02 in virtually all blue HB stars. Using high-precision Stroemgren photometry and spectroscopic gravities for blue HB stars, we find that any helium enhancement among most of the clusters blue HB stars is very likely less than 0.01, thus ruling out the much higher helium enhancements that have been proposed in the literature.