It's an old refrain, often used by UFO researchers when they want to highlight the bona fides of a particular UFO case - military personnel and police officers are "trained personnel" who make for better witnesses, and also of better character, ergo, the UFO case that centers around them is much more difficult to refute.
To which I say (to quote an American general from World War II) - Nuts!
Soldiers are highly trained to do one thing - kill people. They do, of course, have other areas of training as well, but this is their primary function, even in our feel-good age of nation-building and peacekeeping/making.
Police officers are trained to enforce the law, which involves a number of different skill sets, most of them physical, because at their core, the average patrol officer (the vast majority of police officers, and the ones who seem to come into the most frequent contact with UFOs) is in the business of breaking up trouble, or trying to stop it before it starts. They are not investigators.
Most soldiers and police officers are good at what they do. But are they trained any better than Joe or Jane Q. Public when it comes to observing and reporting on events that could be called abnormal / paranormal?
I don't think so, at least not as a general rule. You have to look at the individual soldier, or police officer. For example, there's nothing about the group of soldiers involved in the 1980 Rendlesham case that stands out as being anything extraordinary in terms of their ability to observe events.
Another canard is that military personnel and police officers are somehow immune - or at the very least, less susceptible - to emotions, perhaps even panic, than your average civilian. Again, there is no objective basis for this conclusion. It depends, at the end of the day, on the individual, and the circumstances.
For example, a Green Beret might have nerves of steel, but a cook, or even a military policeman, might be less steadfast. And one suspects that even the best-trained soldier or police officer can overeact, or panic, given the right set of circumstances.
Doubt that? History is replete with examples that drive home my point. One stunning example can be seen in the case of the tasering death of Polish-immigrant Robert Dziekanski by four RCMP officers in 2007. There are many others.
Stan Friedman is often fond of saying that people are good observers, but poor interpreters. I agree with the latter part of the statement, but not the former. Having served with the RCMP myself when I was in law school, I know first hand how tricky observation can be, particularly under duress, and especially when one relies on memory after the event to reconstruct it. This is the biggest flaw in the Roswell accounts, which were given decades later.
The best scenario - although still not perfect - is for a witness to have made notes immediately after an event, as police officers do. Then you can always "refresh your memory" later, as we used to say when being cross-examined on the witness stand.
But no matter what, any single witness is of questionable value. What is needed is some sort of independent corroboration. Obviously, physical evidence would be best (and there is some of debatable worth with Rendlesham), but other witnesses viewing an event, preferably who are unknown to the first witness, and even better if they're looking at it from a different angle, will do as well in terms of making a case worth studying.
Then there's the character question. Often researchers will imply, and sometimes even state outright, that military personnel and police officers are of impeccable character, and would, of course, never lie, or commit any misdeeds.
Again, history says otherwise. A current and noteworthy example can be seen with CAF Colonel Russell Williams, who has just been charged with multiple murders (note: yes, I'm aware he's innocent until proven guilty). Prior to this, if he had been a UFO witness, he would no doubt have been pointed to by researchers as an exemplary man, incapable of any malfeasance. He was, after all, a respected and accomplished senior commander, whose tour of duty included a stint as commanding officer for Camp Mirage, the secretive Canadian Forces forward logistics base that's not officially acknowledged by the government or military, but has been widely reported to be near Dubai.
This is not to dismiss military or police witnesses, of course. Rather, it is to remind people that no UFO case can stand on just eyewitness testimony, and no eyewitness testimony should be allowed a free pass, or the equivalent thereof, based on what amounts to an appeal to authority.