If I'm not mistaken, it's true that, according to Bernhard (if I'm not wrong; see https://www.pianoforum.net/smf/index.php/topic,8981.0.html), Fink/Sandor and Hanon/Czerny/et al. are BOTH flawed approaches - not just "wrong," (ie having incorrect methods for how to acquire 'technique') but also trying to do something that cannot be done - prescribe technique independently of repertory. Here's what I mean (I think):
Hanon and Czerny teach (I'm not quoting) - "do these exercises many times, and your technique will improve."
In contrast, Fink (whose book I am currently reading/studying) says - "here is how to MOVE in a healthy manner, which will improve your playing, reduce unhealthy tension and the risk of injury"
One is a mindless "recipe" which is mostly useless, even harmful. The other (from what I have gathered so far) is designed to cultivate an awareness of the principles of efficient movement. Are these the same?
Bernhard answers, in short (I think) : They both teach technique prior to, and in the absence of music, therefore they are "misguided."
Excellent answers above. Saved me a lot of writing!

I completely agree with everything said by xvimbi and snitzeln above. I will just add the following:
I do not really put Sandor, Fink, Hanon and Czerny in the same boat. I reread the thread you quoted, and I agree that in isolation it may seem that I do, so here is the qualification:
Hanon, Schmidt, Pischna et al. are the worst. The physicality is completely divorced from the musicality, and the directions they give goes completely against anatomical facts. In my opinion they should be avoided as a waste of time at best and as injury-conducive at worst.
Czerny is very different from the above. Czerny actually has music around the exercising. Unfortunately with a few exceptions most of it is very mediocre music. If you want “studies”, that is pieces of music the stress a particular technique (movement pattern) there are far better choices, for instance like Scarlatti and Bach, and for more advanced stuff, Chopin and Liszt studies. In short, Czerny is simply not necessary. Why would anyone prefer to dedicate time to learn a Czerny study when they can learn a Scarlatti sonata completely escapes me. Of course, Czenry is not the only one doing this sort of thing. Eggeling, Bertini, Gurlitt, Burgmuller, Cramer, Heller, Moskowski are all into it in different degrees of musical mediocrity. By all means learn and work on these studies,
provided you are interested in them as repertory. As long as one enjoys them as music, I say, go for it.
Sandor and Fink are a different thing altogether. First, they do not even mention exercises. All their technical examples are related to actual pieces from the standard repertory. Both books are superb and superbly written, and I am really sorry that Sandor never produced an accompanying video. I cannot recommend these books strongly enough. In the thread you quoted, what I meant to show was that listing techniques was ultimately impossible since different authors would organise the subject in idiossincratic ways, and I used Sandor and Fink as examples of how two different authors, talking basically about the same movements and with basically the same technical philosophy could organise the subject in so totally different ways. Indeed, so different is the way they do it, that I always encourage people to read both books and treat them as
complementary rather than contradictory.
So to answer your question, these three (Hanon, Czerny, Sandor/Fink) are not the same at all. Hanon is to be avoided as truly misguided

. Czerny (and similar) are all right as long as you respect it as music (rather than regard it as pure exercise)

and Sandor/fink are invaluable resources that cannot be recommended highly enough.
At this point, I return to the reason behind my post. I am of course guided by the higher-level question: How does one independently discover the correct technique to play a passage? This with respect to the whole playing apparatus, the entire body. My lower-level question on this thread, is: Will this learned repertory of movements help a pianist to improve?
Suppose (for a bad example, but if I'm not specific I'm sure I will be rightly accused of taking technique out of context) that I desire to learn (say) the Sixth Hungarian Rhapsody (Note: I do not play and am not learning this piece. My question is: how can I DISCOVER how to play it? and specifically, will a study of octave playing along the lines of Fink/Sandor assist me in finding a correct way of playing it?).
I am faced with a huge number of ways to play this passage. I must decide what use I will make of the 4th finger, what position to hold my wrist, how much wrist flexion to use, how much lower arm muscle to use, how loudly to play, how to 'release' the note, .... ad infinitum.
And also suppose that, after isolating the octave passage (in this example), I am consistently faced (say) with wrist tiredness and (eventually) tendon soreness. (I have never actually attempted this piece). Even IF I eventually manage to work the passage up to speed, it is clear that my technique is wrong. Not only will my playing sound "stiff", but, if I persevere, injury will result. Further suppose that I try several ways, but fail, to alleviate this problem.
FINALLY returning to the question: will a more 'pragmatic' teaching approach (being told how to play these octaves) such as studying the specific methods of a good teacher (in this case Fink) produce superior results to trying to discover how to play this passage from 'scratch?' (From here it's only slightly a stretch to ask, can a teacher help with technique at all? Mine does rarely, if ever. But that's not the question.)
Apologies for such a long question. I'd appreciate hearing what everyone thinks.
As for this question, I think xvimbi pretty much covered it all. I will add that a lot of piano technique comes from lateral thinking. If you are a good lateral thinker, you have a very good chance to figure it out for yourself. If you are not, you may spend years doing something that does not work. And then you may find someone who in five minutes shows you how to do it. And you feel like kicking yourself for not having figured it out yourself.
And yes, a teacher can help enormously with technique – if they are so inclined. A lot of famous teachers are also famous concert pianists. They may have acquired their technique very young. It is usually mostly at the unconscious level.
They do not know how they do what they do, even though they can do it superbly. This kind of teacher is either impatient or unwilling to help in technical matters. They want to concentrate on musicality. Liszt was such a teacher. He expected you to come to his master classes having done “your dirty laundry” in his own words. There is nothing wrong with this kind of teacher, provided you already have the technique. Very often these teachers will have assistants whose job is to wash the dirty laundry with you. Beethoven didn’t have the patience to teach his nephew Karl, he sent him to Czerny instead. Claudio Arrau likewise, had assistants to work with pupils before coming to him. Other teachers thrived on technical matters – Dorothy Taubman and Abby Whiteside come immediately to mind – so it really depends on your own level.
Have a look here where I discuss this particular (teachers) subject more fully:
https://pianoforum.net/smf/index.php/topic,2450.msg21250.html#msg21250(the four levels of teaching: Toddler, beginner, intermediate and advanced)
I suggest you ask your teacher about it. Some teachers tend not to delve into technique if the student seems to be doing fine, however when asked about it, they gladly offer guidance. The worst that can happen is that s/he will assign you Hanon

.
Best wishes,
Bernhard.