If the media does not contextualize risks correctly, as it never does, it's absolutely a crisis—a crisis of a poorly-informed, panicked society lashing out and doing irrational things.
It's not a costless error if a warped illusion of risk drives countries to, i.e., deploy nuclear-tipped space weapons for asteroid defense, which then precipitate a genuine crisis. It's not obvious that having more defenses is obviously safer than having less; some thoughtful people have argued the opposite:
>"In our view, development of this asteroid-deflection technology would be premature. Given twentieth-century history and present global politics, it is hard to imagine guarantees against eventual misuse of an asteroid deflection system commensurate with the dangers such a system poses. Those who argue that it would be prudent to prevent catastrophic impacts with annual probabilities of 10^-5 would surely recognize the prudence of preventing more probable catastrophes of comparable magnitude from misuse of potentially apocalyptic technology."
https://sci-hub.se/https://doi.org/10.1038/368501a0 ("Dangers of Asteroid Deflection" (1994), Carl Sagan & Steven Ostro)