Probably less so than you might think.
It is the responsibility of the cat owner to keep it from being a nuisance or damager of property to those around it. If the owner neglects said responsibility, and animal control is unresponsive, what's a property owner to do?
Not shoot with an arrow that's for sure.
Oh don't bother, Sungirl and she have already decided you are, no amount of explanation will change their minds.