As an EMT this is extremely poor advice. Speaking from a medical standpoint you are robbing us of any opportunity to make a game plan and mentally prepare for scenarios inside the confines of that particular dispatch. If all we hear is "blah blah rescue nature unknown", we go in blind. The same thing goes for LE, they are still going to arrest you no matter what you say, but if they know who and the what, you can avoid complications.
For instance, you say there's a shooting and hang up, they may stumble upon you holding a gun to an injured person on the floor. At that moment you stand a decent chance of getting shot yourself. Do not hang up on dispatchers, the information they gather is vital.
Cops rely on information like we do, a call for a shooting in self defense gets them in a vastly different state of mind than a call making them think they're about to engage in a fire fight. This is actually coming from someone who has been to the scenes of shootings, I have been in the court room and I have seen the outcomes of cases involving numerous scenarios.