Dubious.
Certainly, behavior is driven by perception of danger, but whether perception of danger generally tracks with actual danger or not is…less certain.
I know for child abduction and child assaults by those outside of the family that has historically not been the case; and perceived danger has increased as media focus increased despite decreasing actual danger, for several decades in a row.
I don’t see why similar (or opposite, if media focussed shifted away while actual danger increased) trends would occur with other forms of danger.
It wasn't presented as a counterexample, it was presented as grounds for doubting the mechanism for the effect you describe.
Increased danger -> increased perceived danger -> behavior which attempts to mitigate danger is a nice theory, but it relies on deltas in perceived danger corresponding to deltas in actual danger.
If deltas in perceived danger that manifestly do drive behavior are driven by processes that are independent of actual danger, your argument no longer makes sense.
Urban violence (such as in Chicago and Minneapolis) might have something to do with it.
[0] https://abc7chicago.com/chicago-police-homicides-murder-repo...
[1] https://www.startribune.com/staggering-surge-in-violent-carj...