To be fair....there have been several instances of F-16's having rather serious un-intentional landings that did not result in fires.
As most Fire Sprinkler systems are ceiling mounted and require steel. piping for the water supply....I cannot imagine the system did that much good where the aircraft came to rest.
Generally, they are installed in "circuits" so the loss of integrity of one part of the system does not cause the entire system to fail.
Likewise most sprinter heads require heat to trigger them.
The Accident Report will have some discussion about what role the sprinkler system played in this event.