For instance, I was in the Marine Corps in the long ago. In advanced training, I received about two hours of 'training' with the M1911A1 pistol. Most of it was 'keep the muzzle down range' in various colorful language, the next popular subject was how hard the thing kicked and how inaccurate it was; and I think they devoted ten minutes or so to lining up the sights. Then we were directed to the firing line where the pistols were on the bench waiting for us - we didn't walk with them in our hands at all - and I think three pre-loaded magazines with five rounds each. Shoot the ammo and get off the range.
I left a M1911A1 pistol at home when I enlisted and had some idea of how to work it. I was the one eyed man in the land of the blind.
Same with the rifle. We were more seriously trained with the rifle (an M14 in my case). We were 'exposed', or 'familiarization fire' to M60 machineguns and 3.5 inch rocket launchers and LAAW rocket launchers. Very limited.
I am not sure what your MOS was, but I do know your experience was far different than mine. I've probably put down 10s of thousands of rounds through various weapons, to include at least a dozen rockets and a few hundred rounds through a Mk-19. Of course, I was an infantry MOS. I also happened to be a squad leader in a good unit. Myself and other squad leaders convinced our CO that cross training (real cross training, not "familiarization") was valuable. Knowing how to pull the trigger on a 240 isn't that hard. Knowing how to set it up and lock it down on a tripod, along with making adjustments given by the A-gunner, takes a few trips to the range. We had that opportunity.
With this being said, the devil is in the details. I'm sure the OP meant "just because someone said it came from military, LEO, etc, don't take it as the gospel." This is true. The military is full of good people with important jobs that will likely never have to fire a gun in a conflict. Hence, they don't particularly train much for it. I do believe ALL LEO's should be able to give basic marksmanship advice. They don't have to be expert on everything that is firearms, but if they can't explain to someone how to shoot accurately then they are a walking liability. Yes, I know there are thousands (if not 10s of thousands) out there. That should be remedied.