The C system has three independent pumps powered by two independent sources. Therefore the only likely way for the system to completely fail is total fluid loss.
The landing gear has a Alternate system which relies on electrically releasing the three landing gear uplocks and allowing them to fall under gravity. You cannot selectively lower each landing gear via the Altn system so in all probability the entire Altn system also failed.
On the face of it, there must have been multiple failures on this aircraft. C hydraulic system, Altn Landing gear system? The question will be why.
Great landing by the crew, but I'd hold off on lionising them until all the facts are known.
I am a glider pilot too... but knowing how to fly a glider probably contributed very little to the safe outcome of this incident.