Crying wolf is normally starting the operation while there isn‘t a wolf.
This is misdirection while there is a wolf
Similar but different
This is misdirection while there is a wolf
Similar but different
That's not pedantic, that's the meaning of the idiom.
/joke
But have you considered that the criteria arose organically as opposed to being engineered top down to account for edge cases such as this? I think in practice the term can probably apply to any instance where you might consider the longer term reputation of an individual or group that is separate from the response team.
Basically you've decided the two things must be mutually exclusive but haven't provided any reasoning or precedent for that constraint.