That sounds highly, well, wrong. OSHA probably has something to say about it. Talk to the Boss!
Anyhow, I've always feared I would be told the same just like I was told I couldn't bring a bike to work because of "liability" (W(hatever)TF that means). I avoided the bike problem by getting a folder I bag in the morning
and have avoided any clothing issues by arriving before anyone else and, incidentally, leaving nearly last if not last too.