In a false fire alarm you have the emergency services responding, possibly pulling them away from real emergencies, possibly fire suppression systems engaged adding property damage and cleanup, and everyone evacuating the premises wasting peoples time.
For a crowd-crush protocol I’m imagining something like this. If you see someone being crushed or fallen down and trampled you raise your hand. Possibly with some hand signal like a fist with an extended pinkie finger to disambiguate other reasons to raise a hand (like dancing at a concert for example). If you see someone giving the crowd-crush signal you also give the crowd-crush signal, this way it propagates throughout the crowd. In addition to giving the signal you will also stop moving and stand in place until the issue has resolved. At most a protocol like this would waste a few minutes of peoples time in a false positive.