Well it's definitely a false alert but I think maybe I see what's bugging you. If an enemy agent intentionally did that with the goal of disrupting operations we'd call it misdirection and it seems a bit silly in that scenario to also categorize it as crying wolf. Since there's an ongoing search that the guy was aware of you view this the same way.

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.