Wow. I'm glad you made it out of that situation safely with no one hurt.
I teach the "negligent discharge" terminology, whether it be to military, law enforcement, or civilians. Accidental discharges are very rare, but it should result in no one being hit because we keep our weapons pointed in a safe direction. Even if you had the purest of AD's (ie "slam fires"), the gun wouldn't be pointed at someone when it would have occured.
As far as your original question:
I was never taught to pull the trigger, until on target and ready to fire. Not in the Police Academy, SWAT training, or Firearms instructor school. I don't want to say that this is wrong, but I don't know who is teaching this, and it is obviously causing AD'S.
Unfortunately, the military is... and I adamantly disagree with it, along with the whole "unloaded weapon" philosophy. Here's why:
The military is real big on "clearing barrels", which is a barrel full of sand. When a soldier/sailor/airman/marine (from here on out referred to as "soldier") enters a building (even in Iraq "inside the wire"), the soldier is supposed to check/clear the weapon, then "verify" the weapon is cleared by placing the muzzle into a small opening on top of the barrel, and...
...PULL THE TRIGGER!
When the hammer falls, it SHOULD only go "click", but if it does go "BANG!", then the soldier faces punishement for the ND, but it ensured no one got hurt.
My big disagreement with the clearing barrels are the fact that the military is promoting complacency by making soldiers carry around unloaded weapons. If all weapons were loaded at all times, the soldiers would have more respect for them, and that would cut out a LOT of horse-play I have seen, and my friend SSG Berry would still be with us today.
In October 2005, I had been out on patrol all night, and was sleeping in my tent. At a little after 7am, I was awakened by a loud "BANG!" In the tent next to mine, another NCO asked SSG Berry if his "weapon was loaded" because he saw a magazine in his 9mm Beretta. SSG Berry pulled the 9mm and pointed the muzzle under his chin and said, "if it would loaded, would I do this?" The next thing SSG Berry did was DIED.
A loaded weapon kept in a holster doesn't accidently go "BANG!" When I'm in a classroom, I feel more comfortable knowing every single holstered weapon is loaded as opposed to "guessing" if every weapon is cleared. I can't change the military's way of thinking, but in *MY* classroom, all holstered weapons MUST be loaded, and we train with "blue guns". There's no question or doubt that way.
Wow, I was on quite a soapbox with this post... sorry about that.