I would argue that has nothing or at least not much to do with riding a fixed gear. You may not able to brake as quick as a rider with proper brakes but this seems not to be the point in this acciedent. People walking on the bicycle path without watching, even without recognizing it, people are playing with their smartphones ignoring traffic at all. On my daily commuting way of about 20km through Berlin I am watching so much stupid behaviour in traffic from cyclists, pedestrian, car driver, ... At least twice a week I find myself in dangerous situations I didnt cause and couldnt prevent (and I drive mostly with my kids and therefore pretty cautious).
Riding, walking, driving with cautioun and careful would help to avoid such situations.
PS: I stopped riding fixed gear as a car in front of me just started its engine a second later as expected, I couldnt brake anymore and nearly hit its rear window - what I decided to do was to fall on the road rather into the car...