I have been riding brakeless for several years. Only knee pain I have had has been when my pedal position was incorrect or I pushed big gears.

I think using lower gears, proper bike fit is and good genetics are all important.

When it comes to most serious athletes, knees and ankles are the first to go. No one in my family has ever had knee surgery. If you have knee pain on a fixed gear bike and none on a geared, listen to your body and don't abuse it!