I think this is why it's so important to find the essence of the art for yourself. I personally hate the "closed door" mentality because it stifles the art. However, the deep truths are not taught, they are discovered...that's to say, even if I teach someone a very profound concept, their ability to internalize that truth is very much dependent on their "martial arts IQ" so to speak. Some people are gifted in math, and the answers come easy to them - they even develop their own shortcuts and blaze a path for others to follow - however this is not something that can be taught, it is something they are born with. I think the same holds true for anything, and especially martial arts, where the results speak for themselves.
My post is only tangentially related, so if you don't feel like reading it, you don't have to.
I get what you are saying, and I think that it is ok as internal dialog for a martial arts instructor so that his ego is protected when his students don't do well. Math, like martial arts, can be taught. I don't believe a whole lot in natural aptitude as a determining factor as I do training and starting point.
If you were in the 2nd grade, and all of your reading assignments were at a 6th grade level, how good do you think you would get at reading? Probably not very. The problem with martial arts is that everyone is at a different level when the come in and martial arts instructors have a limited ability to teach to each person's level.
The same is true for math. When I got into the end of calculus in college, I hit the only class I ever couldn't beat on the first try. For some reason I had not gotten some of the background math in a previous class and the shit you do with special coordinate systems is difficult. I killed infinite sequences, but the polar and vector killed me. I had to drop and retake it. When I got to calculus based physics though, it was a cake walk. I could derive the formulas myself, because my math teacher gave me a great base. If things are over your head, it looks like you "don't have natural talent," when really you missed a basic skill and people are talking over your head because your training skipped a step.
The natural aptitude in martial arts is derived from a few different things.
Athletic Ability
Ability to Pay Attention
Time Spent Imagining Oneself Fighting
Visual Learning Ability
If a student isn't actually interested enough to pay attention, and doesn't empty their mind of T.V. and social events and video games while you are talking, they aren't going to learn it.
If they have the desire, your instruction needs to be on their level. Martial arts classes are usually about parroting and often the people who parrot best only do so because they were already in shape when they got there, visual learners who have already conditioned themselves for the activity by spending time imagining themselves do it - often by watching other people fight.
So a new person who doesn't have the "natural aptitude" but wants to do it can be taken to a high level by building up not just their body, but their mind, by having them watch fights actively, imagining themselves in the role of the fighter, giving them information on self defense to put things in context, and demonstrating technique with you (the instructor's) ass on the line in front of class - all these things to bring them up to the level you expect them to be at so that you can talk to them at the level you normally teach to.
Once they build up their athletic qualities and spend some time learning about the context of fighting by watching people practice, watching people fight, watching experts compete with one another and visualizing themselves in that role, they will be able to learn martial arts.
If you take someone who has a desire to learn but are not developed enough for the basics, and you start spouting off platitudes about being like water and expanding when your opponent contracts, and how to go for eyes while the other persons hands are busy and all that horse shit, you are going to be talking over their heads and wasting their time.
I personally find it offensive when the "deep truths" or "black belt material" are held back like secrets when I am personally capable of learning them, because I know that the reason they are holding it back is because most instructors could write all of their A-list material on two sides of a 8x11 sheet of notebook paper and spend all their time looking for ways to drag it out. They are quick to spout it out if they think no one around is capable of learning it, and probably the fastest way to get it from them is to play stupid and trip over your own feet so that they feel comfortable showing off. Those same guys, inclined to "secret moves" are quick to get really fucking conservative when they think someone good enough to parse through it is around.