Sorry about the first line of my post.
You're right in the sense that he should have brakes. But that completely defeats the purpose of the fixie, and I'm sure a hipster like OP wants his as a fashion statement rather than an actual form of transportation. Just a front brake poses problems for new fixie users - especially in traffic when they need to stop fast. I've seen idiots come to the shop having actually flipped their bikes at lights cuz of that, so I always prescribe 2 brakes. And if you do that, you might as well turn it into a single speed. It's retarded to have a fixie with brakes unless you're training,