People see the uniform not the face. It is a truism, and it can be weirdly triggered. For example, late August afternoon I went into Staples to buy some office supplies, and I had just happened to be wearing khaki pants and a red polo shirt which unfortunately was exactly the same color as the red 'staples' staff shirts. All through the visit anxious mothers came up to me looking for school supplies for their kids or asking if I could check in back for this or that thing. I would tell them I wasn't working there but one refused to believe me, she said I was lying because I just didn't want to do the work to check for her. I pointed out the lack of logo on my shirt but it didn't help.
In a related note I normally carry a high visibility vest and a blue hardhat in my earthquake supplies 'go bag' in my car. The hardhat was left over from the Hoover Dam tour (which gave out real hard hats as souvenirs!) and the vest I wear when I'm biking. I reasoned that after an earth quake if I am walking home I don't want aftershocks dropping bricks on my head. Several people have warned me though that if you step out into a post disaster scenario with a hard hat and a vest people will assume you have an official capacity and are there to help. You won't get a chance to walk home.