''Exactly what phone calls do the police make to “determine the nature of the report”? Try to think carefully, as it’s a trick question. They can’t just call the other person in the conversation, since he too is implicated in the report and the police would have no way of knowing—on a fucking phone call—whether or not he was just lying to cover his part in the crime.
No one else heard the conversations, but the other guy and the waitress. '
So you think the police are incapable of investigating claims? They could ask the waitress exactly what she heard and in what context, they could ask the guy what he said to his friend, check what the friend heard the guy say, cross reference the three accounts and determine risk.
It should become quickly clear that the waitress was overreacting
It does not appear that you are thinking this scenario through. Turn the tables and imagine that this was a guy actually talking about/ planning to shooting up a school. When the cops call the guy to get his side of the story, they have just alerted the person that they are on to him. Maybe he wasn't planning on doing the deed for another week, now he moves up his timeline, grabs his gun, and heads for the nearest school, not necessarily the one he was targeting before, but rather another one that the he thinks the cops are not watching. Or, they call him up, and he does poorly making excuses on the phone, but he still has a lot of guns and ammo. Now he knows the cops are coming for him, so he can set up an ambush for the police.
In other words, it would be extremely stupid for the police to call a suspect in this situation and get their side of the story. The absolutely must err on the side of caution, pay the man a visit before he becomes aware that anyone has said anything, and if possible remove any weapons from immediate use by the suspect before getting his side of the story. That seems to be exactly what they did in this case.