I assisted YMCA instructors during the early to mid-80's when I was going through the "apprentice" phase of my pre-instructor NAUI training to diversify my experience. I don't remember any set of standards or even a textbook from the Y at that time. No talk of "safety stops" at all then. We used the "Science of Scuba Diving" textbook written by an author I don't remember his name but it sounded like a "Polish name." The dive tables used were US Navy tables. NAUI didn't have its own textbook during these years IIRC. To be honest, my memory is hazy about what happened when exactly, it has only been almost forty years now
I think instructors having command over their own courses was once pretty much the way it was for many agencies.
I did read Al Tillman's history of NAUI and know that they did not have a true central curriculum either. Over the years there have been many threads about how great it was that NAUI instructors could pretty much design their own courses.
When I became a TDI student, the instructor said we would not follow the TDI standards, and we never knew what standards we were following. We just did what the instructor said to do when we were in the water. Eventually I got a bit ticked off and wrote a detailed description of what we were doing to TDI headquarters, and they replied that it sounded like we were getting a very thorough course, and it was all OK with them. When I became a TDI instructor and saw the actual course standards, I saw that the TDI courses I had taken had very little in common with the TDI standards, but that was OK with TDI, as long as they felt the course we did take covered the TDI content somewhere.
I once had a long discussion with a SSI Course Director as we headed out on a boat to a dive site. He was doing final training dives for a new SSI instructor he was certifying. He was peeved that this would be the last instructor he would be allowed to certify on his own; from then on, his instructor candidates would have to be reviewed by an independent instructor examiner. He liked things they way they were, because he could taylor the course to the student. If (as in the current case), the instructor candidate just wanted to teach in a tropical resort, then he could skip all the stuff that wasn't related to that. Now with independent examiners, he was going to have to teach the whole damn course.