It is not working based on approval but based on sensors observing the airplane on final. Even if the plane is landing without clearance, even if the ATC is held hostage by a terorist or having a stroke the lights should turn red when an airplane is approaching the runway from the sky.

This pdf talks more about how it is implemented: https://www.oig.dot.gov/sites/default/files/WEB_Final_RWSL.p...

“RWSL is driven by fused multi-sensor surveillance system information. Using Airport Surface Detection Equipment-Model X (ASDE-X), external surveillance information is taken from three sources that provide position and other information for aircraft and vehicles on or near the airport surface. RWSL safety logic processes the surveillance information and commands the field lighting system to turn the runway status lights on and off in accordance with the motion of the detected traffic.”