I believe a long time ago on Sheldon Brown's site (I forget where.) I read that a front brake can provide all the necessary braking force you need and that a rear brake will give you no stopping force if the front brake is being used as much as possible.

With my understanding of physics, I would think that this would apply to all bicycles, not just fixed gears.

Can someone tell me whether this is right or not?

I understand though that there are other environmental issues that also can influence riding conditions, such as slick roads, etc.