You might want to check how many addicts/drunks/dementia patients get naked regularly in the hospital. It might be so regular that if they see you out of the corner of their eye, their gut reaction assumes it is someone naked.

Wear brown and add a "I'm not naked" sign. Screw 'em

Um, Sweetie? Any shade of flesh coloured clothing that matches your skin tone gives that double take of 'why are you walking around naked?' Fawn coloured leggings are the fashion in my area atm so just for that second until you actually look, there's a lot of 'half naked' teenagers all over the place. If your scrubs match your skin tone well enough then you ARE going to give ANY human brain that double take. It's not an issue with your skin, it's the lag between what eyes see and the brain processing the information. The reaction once the brain has processed it? That you can judge the hell out of. Maybe get some fun stickers to add to your scrubs to interrupt the 'illusion' going on in the human brain? This is an 'every skin tone' issue, white, black, brown, green, pink, blue... If your clothing matches your skin tone, the human brain will see 'naked' for that first second. If your manager was running around in scrubs that matched her skin, she'd be getting the exact same complaint.

Who is the brain-dead idiot who invented brown scrubs anyway? Scrubs should never be any color that looks like skin, pee, poop, or blood (take that, Deep Space Nine surgeons!).