My read of the ATC conversation suggests the problem was its wishy-washy nature. The F16 pilot was kinda-maybe-sorta thinking he just might maybe be seeing the Cessna, and ATC, who didn't want to inconvenience anyone with unnecessary deviations, suggested "IF you don't see the target, immediately turn'.
"F16, IMMEDIATE TURN 180" would have avoided headlines, but no one thought it necessary.
Aside from wishy-washy [as a GA pilot] I find it difficult not to condemn the F16 pilot. If you're allowed to drive a Formula 1 car in city traffic, you have a huge responsibility to not kill too many drivers (and destroy millions of dollars of taxpayers' hardware in the process, though that's small potatoes compared to a single life.)
Bring it on.