Riding fixed doesn't haven to be hard on the knees, but many people make it so.

The 1st mistake is riding overly high gears, especially if there's any climbing. This is common, because gearing lower tends to cap the top end speed that some look for.

There's also significant high stresses involved in reversing torque to stop or resist when descending. All of this can be managed if folks use some common sense, and I, for one, rode fixed for decades, including very hilly terrain, without any long term damage.