One can't investigate every threat. You have to prioritize. Part of prioritizing is determining how much damage can be done with the resources available to the person.
If someone says "I'm gonna bring down the Golden Gate Bridge with this 12" stick of balsa wood." you don't give them a second thought. They may have hostile intent, but they clearly lack the understanding of how to, or the means to[0], cause harm to the bridge.
If someone says "I'm the operator of this container ship full of high explosives and I'm going to ram it into the GG Bridge and detonate the explosives.", then you investigate that, as the person very probably has both the intent and means to cause actual harm.
We -as a society- used to refuse to be terrorized. We used to laugh off incredible[1] threats as the insanity, bluster, or cathartic ranting that they clearly were. We (or maybe just our investigative and enforcement organizations) freak out much more over much smaller things these days. Our society is poorer and weaker because of this.
I hope that encouraging people to learn to put threats into perspective will help reverse this trend. Perhaps a calm, level-headed populace will calm its over-reactionary leaders, investigators, and enforcers.
[0] Foreign Object Damage. In this case, at-speed impacts with grit, ice, and whatever.