The difficult question is "what is proper instruction?" As far as I know, there are only personal assertions about that--no hard facts. What is "proper instruction" is only someone's opinion--or the opinion of a group who have gotten together to claim that their opinions are "proper."
Once again, you get caught up in the false belief that the only way to prove value to anything are "cold hard facts". That phrase in and of itself can't be proven, realistically. What evidence one person examines and concludes is accurate, another person can similarly deduce that it is non-sense. (I believe we've gone down this road with you a few time recently, regarding something else. Or are your arguments in this thread related to that "other" argument?)
In other words, who decides what is "fact" and what isn't?
The bottom line is that in almost any athletic endeavor, there are instructors who can and do teach people how to perform better than they would have otherwise. Or at least in a shorter time-frame than they would have if they had to figure it all out on their own.
You make a valid point in that anyone can proclaim themselves to be an "instructor". This is where testimonial evidence is helpful, because those who have been taught by said "instructor" are the only ones who can propely assess the value of their teachings.
I used to study karate, taught by an instructor. A 5th degree black belt. (There is no "formula" for that, either, only the judgement of other "instructors".) I can easily tell you that I could never have learned how to execute the things you need to do in karate without instruction. I could have watched grand masters from a distance of 5 feet for years and not have understood "how" to do what was necessary, without instruction. Similarly, for a short period of time I was considered an "instructor", because I taught kids karate at a YMCA. There is a world of difference between the instruction that I received from my sensei, and the instruction I gave my students.
How do you determine that? You cannot find any computerized formula for who is an accomplished instructor at anything. You cannot produce "cold hard facts" other than the results shown by that instructors students.
I will get some serious pool instruction at some point in my life, when time, employment and finances converge appropriately. Because I know the value of good instruction. GMT will never do so, becuase he has no cold hard facts. And he will lose out because of it.