A trip to the sports doctor
(Tl;dr, go to bold sentence.)
I visited the sports doctor today because I've had knee pain when I sit for long periods of time (e.g. class). I've been riding single speed for about a year, and fixed for about two weeks (and commuting for the last two years). But I figured my knee pain had less to do with that and more to do with my frequent exercise at the gym, especially squats/lunges/jump squats.
Anyway, I have runner's knee (patellofemoral pain), easily treated and likely fixed by daily stretches. Doc said it happens in men when their hamstrings are tight, and to women when their quads are weak.
Here's the part to care about. I told her that I'm riding fixed. She knew what that means; she rides bikes too. I asked if it was detrimental to knees and her answer makes sense. Riding fixed is just as likely to cause knee pain as riding any bike habitually for years. She confirmed locking your knees to skid isn't helpful (which I seldom enjoy/do anyway).
Overall, yes knee locking is more likely to hurt ya. No, riding fixed does not necessarily equate to worse knee pain than a roadie or MTB rider might develop.
Granted, this one doctor's opinion. Nevertheless, it's a sound, educated opinion.