...Of course, if they were part of an agency whose objective is to respond to emergency situations, there's also the chance that they could get charged. It would be under "negligent homicide" or something like that.
The agency's lawyers would put up a good fight over that one. Blowing off an emergency call on the phone is one thing. Having some unauthorized and unknown person calling in on the radio is another matter entirely. A lot would depend on how coherent the distressed caller was, and if a location was easily obtained. And under those circumstances, a good cop would probably roll in ready for an ambush, further slowing the needed response.
You see the problem here?
Years ago, I was unlucky enough to hear a distress call on Marine channel 16. It was a man claiming to have been kidnapped, and then shot, on his boat off Santa Barbara. (google 'Chronic B*tcher' and 1979 for a link to the story)
A bunch of us were sitting around listening in amazement, but almost 100% sure it was a hoax. It just didn't sound real. The Coast Guard did take it seriously, especially since it was on the distress and calling channel.
Now take that same sort of call and put it on a police or fire channel, where the normal call intake is done by telephone. Would it be negligence to assume a hoax? I don't know... We sure thought it was, until the papers hit the next day.
Some unprofessional 911 operators already went through that.
All of those cases that I'm aware of involve calls received via telephone.