I write this post having been involved in firearms training for going on almost 20 years now, and having just come off a 5+ year stint with my agencies firearms training staff (we're a large metro agency). I've been to a lot of classes, taught a lot of people, and had the opportunity to work/train with a lot of folks who have been in gun fights in addition to personal experience.
Not all good shooters are good instructors. Not all good shooters are good gunfighters, most in fact aren't. Not all good instructors are good shooters. Not all good instructors are good gunfighters, most in fact aren't. Not all good gunfighters are good instructors, most in fact aren't. Not all good gun fighters are good shooters, I don't have enough first hand data on this one to say where the majority lie.
If you are going to training to LEARN how to shoot better, instruct better, or gun fight better, you need an excellent instructor. It doesn't matter if they themselves aren't a world class shooter, or a former member of a SF unit. If they are an excellent instructor they will make you better at the area you are there for. Front Sight, Gunsite, Thunder Ranch, Shaw, Rogers, etc. all have excellent instructors. Particularly when you're looking at basic and mid level courses. Most of the issues that many find to be dogma (trigger types, stance/grip, slide manipulations, etc) are a very, very small issue in a gunfight. The ability to run the gun with competency, and to get the rounds in the vicinity of where you aimed them will handle 95% of the "gun" part of the gunfight, which is about 15% of a gunfight. The rest is tactics, physical conditioning, mental conditioning, etc.
Excellent instructors can be found outside of the big schools, but going to a big school gives you a venue with a by and large vetted staff and curriculum. Are there disagreements on what the different schools teach, absolutely, but for 99% of the gun owning public it will still be plenty to address that 1% of their students who get into an armed confrontation. As a professional LE instructor working at a ~2000 officer agency, I had no restriction on what technique I could teach if it was effective. The odds of one of my students being involved in a deadly force incident is FAR higher than any civilian class, I would venture. I usually spent half my day arguing some esoteric point about support-side thumb slide release activation versus strong-side thumb slide release activation or something similar with my fellow instructors. At the end of the day though, 99% of our students just wanted a single technique they could use that would be effective, and the civilian world is the same.