The episode is pretty specific that the safety beam is an independently controlled safety system, presumably likeakin to the remote detonation sequence on the Space Shuttle. In the event that the crew are incapacitated or their primary controls fail (in this case, due to radiation), the crew on the ground can trigger this system externally by means of a "safety beam".
If I had to guess, I'd assume that the retro backup system was situated at the back of the ship (close to the main engines and facing the Earth and where the radiation would be at the least), whereas the primary controls are located at the front of ship, where the radiation would be at its strongest. This would explain why the safety system still works but the primary controls don't.