Friction doesn't work that way. The station as a whole keeps it's angular velocity so it returns to its configuration if you reset the position of the dock. The only change possible is when a craft docks with the station. That would be a tiny change and could be offset when the craft launches.
No, he's on about the central part remaining stationary i.e. no rotation whilst the rest of the station rotates. There would have to be at least one part of the non-rotating part of the station touching the rotating part, leading to friction between the non-rotating part and the rotating part. This would lead to either:
A) The stationary part rotating with the station or
B) the rotating part of the station becoming stationary
So you'd have to keep expending energy preventing the friction from counteracting what the station is doing. You could have the central part rotate with the station until a ship gets close, but that only minimises the friction, it doesn't remove it.
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Any friction would exert an equal and opposite force on the docking ring and the rest of the station. So the angular velocity and momentum of the station as a whole would remain unchanged. Likewise when you accelerate the docking ring to get it to slow down to stationary (i.e. accelerate it in the direction opposite station rotation) an opposite force is applied to the rest of the station so the station as a whole maintains its kinetic energy.
There is an even simpler way to understand this though. Just apply Newtons first law, a body in motion stays in motion without an outside force. The station as a whole is a body. So the station as a whole is not going to have it's motion changed unless an outside force acts on it. Internal forces can act on the station until the cows come home, that wont change the
overall energy of the station. So if you slow down the station slightly by walking in the direction of the rotation that only lasts as long as you are walking. As soon as you stop walking, the station returns to it's original speed.
I guess that means there would be tiny fluctuations in the speed of rotation throughout the day but even together they would be too small to measure because there is no net change over time. The only noticeable changes would be if a ship docks with the station, giving an outside force. But that outside force could be very carefully measured before it even happens so by planning launches and landings you could maintain the station's spin.