We have no evidence that surgeons scrubbing before donning gloves makes sense either. In fact, there's an undergraduate experiment where people scrub for up to 3-4 minutes and swab after every 10 seconds and plate the swab. The plates actually show more colony-forming units until about 3 minutes, which is much longer than most surgeons scrub. Which suggests that the scrubbing actually liberates bacteria found at the margin of the stratum corneum.