I must have been taught epaulement very early in my training because I never remember having to think about it, and never remember being correctly "placed". I just did it. And loved doing it. And yes, I do remember it had a lot to do with torsion and tension, efface/croise, shoulders, eyelines/chinlines, AND extending line. From my reading of this thread, I also agree with most posters concerning which schools taught it, and which didn't. I experienced the same thing. (It's probably why I was never that comfortable doing Balanchine. Today, if I love NYCB, it's not because of their epaulement.)
After being away from viewing ballets for almost ten years, when I finally was able to see live performances again, I started analysing what I saw at ABT, especially its vaunted male dancers. (I was still familiar with its female principals, most of whom had been at ABT for ten years or more.) And then I started analysing one dancer, trying to see what he did, how he did it, and why I noticed. (I was very reluctant to follow the crowd, and wanted to understand the appeal.) I was not impressed by multiple turns or a high jump (I'd seen Baryshnikov and others past and present with same or similar abilities) or any other fine matters of technique I expected of a principal dancer. No, what I discovered was that Angel Corella had the most beautiful epaulement I'd seen in many years. Even if other areas of technique relax or fail, his epaulement never does. If he teaches anything to his new company I hope it's that.
eg. Gene Schiavone's two photos of the same ABT Swan Lake Act2 pdd penche. In one is David Hallberg, in the other Angel Corella. Both are beautiful images of correctly placed dancers, but the epaulement is very different. You can see that same epaulement in Nancy Ellison's photo of the same pose in her ABT 'coffee table book'--actually I think it's a better pic since it's caught at the end, rather than middle, of the movement. I'll try to give another photo example if I can from photographer Jesus Vallinas took of Bayadere later.