Let me repeat what Carmack said...
The game tic simulation, including player movement, runs at 60hz, so if it rendered any faster, it would just be rendering identical frames
the games tic simulation "Including" player movelment. It is not only about the Movment and Physics engine.
This does have something to do with Refresh Rate. Being that regardless of the rate Set, for benchmarking purposes the game will only ever render 60 new frames per second.