ATC V's TCAS

I remember an episode of the TV programme 'Air Crash Investigation' where such a scenario actually happened. Two planes collided a cargo plane and a plane with a class of russian children on if I remember rightly ❓ The air traffic controller was by himself and engineers were doing something to the radar, which slowed it down. The two planes were on a collision path with each other and the TCAS in the cargo plane told them to descend, but in the other plane the TCAS told them to climb (obvious I know). However the other plane was told to descend by ATC rather than the TCAS command of climb and as a result they both descended then collided. If TCAS had been followed both planes would have avoided collision.
Many pilots are trained to follow TCAS in emergencies, but in the above accident the russian plane was told to follow ATC commands. I hope things have improved now and that all pilots are told to follow TCAS, but I don't know.

Horrible accident that

I remember the father of one of the Russian children hunted down the air traffic controller and stabbed him to death

http://en.wikipedia.org/wiki/Bashkirian_Airlines_Flight_2937

Very tragic and its that episode that made me question what FAA/CAA rules say today about ATC and TCAS in a similar situation. Its very sad about the controller too because he never actually did anything wrong although his workload was abnormally big at the time and as you say the equipment he was using was undergoing maintainance and giving erratic readings. A very sad episode of Air Crash Investigation not only because there were no survivors but because one of the aircraft was carrying mostly children. I'll have a browse through the law books to see what the procedure is today.

That's correct, the pilot follows the TCAS avoidance indications.