The proper way to carry a 1911 style is cocked and locked, period. It was designed to be carried with a round chambered, the action cocked, and the thumb safety engaged.
The proper way to carry a DAO or DA/SA semi is decocked on a chambered round. You may or may not engage the external safety if one is available. In modern semi, the firing pin cannot impact the primer unless the trigger is pulled.
The proper way to carry a modern revolver with a transfer bar is with all cylinders occupied (contrary to NRA instruction, which advocates having an empty chamber under the hammer -- which is necessary on old-style revolvers with the firing pin integral to the hammer).
I don't think your information regarding NRA instruction is entirely accurate. Monday night I attended a handgun proficiency course at the local shooting range. The instructor was NRA certified, and I asked him this very question. He gave me the same answer you just gave above. Perhaps he was only speaking for himself, but he didn't say that the NRA position was any different.