Considering that in the instances of 'high profile' individuals, for whom their treats actually got police attention, and when then deemed 'non credible'; there is going to be a vanishingly small percentage of times in which any action is taken by law enforcement for which the reporter will be satisfied.
What is actually a problem condition is that there is a low SNR and something actually happens to someone, and then police hyper react.
We can only hope that well-trained (larger?) law enforcement agencies know how to sift thru all the chaff, but some small town PD? No way to know what you are going to get there.