I train at a Martial Arts gym that teaches a variety of disciplines for self-defense/fighting etc etc and a couple of weekends a month they train the IPTT (Israeli Police Training Tactics) which means that they train to carry on an empty chamber. I should say up front that this is a pretty legit fighting gym. There is no AC, no mirrors on the walls etc and if you are afraid of getting hit, you are in the wrong place. So my respect for the instructors is pretty high. However, the instructor likes to talk about how the Israeli "special forces" carry this way(on an empty chamber) and that its "actually better" to carry this way because its "safer". With all due respect to him, he is badly misinformed.
I have also watched some of the training go on and I just keep my mouth shut and go on about my business, but there is some really bad training happening. (They do dry fire and rubber gun drills at the gym, live fire at a range) For starters there is a lot of assuming that the "bad guy" is 20 feet away. That is not reality. The bad guy doesn't stand there with a baseball bat and announce himself. Violence happens up close and it happens extremely quickly.
Further, they train that once the bad guy is down you run up to them and shoot them in the head with a follow up shot. This would probably be ok in Israel because their bad guys are legit terrorists, not criminals as we know them. They simply do not have our level of street crime etc., which is one of the reasons (but not by far the only reason, that they carry on an empty chamber) In the US however, if you get caught shooting a downed person in the head you're going to have a lot of explaining to do. Especially if you're a cop. Adding to this problem is that they are teaching this to civilians, most of whom have very little prior training.
What the instructor and people that carry on an empty chamber do not take into account is the history and reason that Israeli guys carry on an empty chamber. It's not because its "better" it's because of their history of having to take whatever firearms they could get in 1947 and not having one uniform way for everyone to carry. Plus, prior to that military officers in armies all over the world were trained to carry on an empty chamber. Keep in mind, however, this was during the era of trench warfare and shooting the enemy at a long distance, not with cops or civilians dealing with violent crime. I'll let you do your own research on the rest of it.
And yes, I know how to chamber a weapon with one hand off of my belt/boot etc etc, but that's incase I'm injured, not because it's a good idea. Guys who carry on an empty chamber simply lack training and, again, shooting paper targets is not training. "It's always been fine for me", is because you've never had to actually get into a fight. Drop your ego and get some actual training from a competent instructor.