Well, for a change, this is definitely in my field of experience, so I hope I may be of some help. (Funny thing I just got done PM'ing JD about this to a point and since I saved the post for future use, I won't have to do nearly so much retyping. Grin.)
Back in the 70's, there were quite a few "Experts" who POUNDED on hammers set on the half cock notch to "check them for safety" in the North South Skirmish Association. Can't begin to tell you how many good locks and trigger jobs those idiots ruined. Knowledgeable people didn't do that, but there were plenty of "Experts" who did. Those of us who worked the guns brought it up to the firearms committee and we got that stopped eventually, though there were still an idiot here and there who did it. I actually found a reference in an Original Confederate Ordnance Manual in the collection of the National Park Service in Fredericksburg, VA library that clearly stated NOT to do such a thing. Of course, this came from the earlier U.S. Ordnance Manual. So it was something enough "experts" had messed up even way back then. That information helped turn the tide so the Firearms Committee wrote some strong rules about it and stopped it at the inspections at the Nationals.
OK, so I began reenacting as a Confederate Marine in 1980 and DANG if they weren't also pounding on hammers at half cock during the safety inspection. (BTW, a few "experts" who inspected guns used in living history at the National Parks did the same nonsense back then.) Since I had already been the junior armorer on THE Marine Corps Rifle Team and was known for working reenactor guns, I started to get that changed. When I formed and Commanded a Virgiinia Infantry Company, I actually got to "be" one of the Inspectors and spent the next couple of years teaching others not to do it. I have a good story about the inspections at the 125th year anniversary reenactment of 1st Manassas (or "Bull Run" if you are from the North) but that will have to wait for another post.
I even caught one "inspector" at the World Championships doing it in 1996 at Wednock, England. Though in his case, I'm sure he knew it would hurt the locks and he was doing it deliberately to break other competitors' guns as we knew that about him from years past. When he broke one of my shooter's original Rogers and Spencers Revolver half cock notch and I found out, I was so mad I was stomping towards the inspection tent to take his scalp. Forunately the U.S. Team Captain saw me before I got there and I explained it to him. He told me it was better if he complained officially than if I confronted the guy, so I backed off. I did see that "inspector" later on by himself and since I was the only Armourer there from any International Team, all the shooters got to know me by my face. I confronted the guy and told him if he ever broke another gun from one of my Shooters or ANY shooter on any Team, I would break something on him. He took me seriously.
When I got back into Rev War reenacting in 1998, DANG if some of the safety inspectors were pounding on cocks set at half cock there as well. Once again, I began an unofficial program to instruct others on how not to inspect locks.
OK, so where did the test of putting the hammer or cock on half cock and GENTLY lowering the musket and hanging it by the trigger come from? To be absolutely honest, I'm not completely sure, but knowledgeable firearms inspectors were doing that at the NSSA Spring and Fall National Championships in the 1970's. I was taught that by a Mentor in the same time period. I believe the test originally came from an original Pre Civil War U.S. Ordnance Manual, but I can't prove that. I don't remember if it was in the original Civil War period Union or Confederate Manuals, but I'll try to dig out my copy of the Confederate Ordnance manual and check that out.
TOF already made good points about the procedure of hanging the musket on half cock by one finger on the trigger. It is not, nor ever intended to be an absolute test, as we all know a half cock that was good can snap off when just the right conditions exist or just from long usage and wear. What it DOES do is show the half cock won't work at all if the cock or hammer slips off the full cock notch. As TOF mentioned, because trigger pull weights on the both Civil War and Flintlock muskets are often heavier than the weight of the musket. What is ALSO shows is if the reenactor himself messed up his lock and it is not safe. Trust me, that happens all too often with reenactors though it is not "common" by any means. You get enough reenactors and the small percentage of ones who do it, just give greater numbers of it happenig. It usually comes from ignorance and from people who don't actually shoot live rounds from muzzleloaders. I've known some Civil War reenactors who have shot over 10,000 blanks and only fired a few live rounds or never fired a live round at all.
Even though we don't directly aim at opposing reenactors closer than 25 yards (at that range and shorter distances we aim over the heads of opposing forces OR move off to beyond 25 yards. Hand to hand combat reenacting is almost never allowed unless the two opposing forces have worked it out VERY WELL before the reenactment and even then - many events won't allow it) even so - if the half cock notch fails, it could injure the person firing the blank round or, people around him.
People who only hunt or shoot competively don't treat their guns like reenactors do because they aren't simulating combat and the stress on the guns that brings. Reenactors have developed a long string of safety precautions to keep unintentional accidents from happening and this is one of them. We worked that out in Civil War reenacting in the early 80's on a more formal scale than had ever been written down before.