Forgot to add:
1) Pischna exercises (more holding exercises). By the way, holding exercises are effective precisely because they take hand movement - up-down, rotation, etc. - out of the equation by "immobilizing" it, thus "forcing" the articulating finger(s) to work, and work independently. (Yes, yes, it is possible to keep the hand relatively quiet without tensing - notice the use of quotation marks around the word "immobilizing".)
2) Practicing scales is, of course, essential, but practicing single-note scales is a particularly poor way to develop the 4th and 5th fingers. Why? Because in each octave you play 1-2-3 twice, 4 once, and 5 only once no matter how many octaves you play.
3) I've had a lot of teachers in my lifetime and I can safely say that level of playing of a piano teacher has no guaranteed correlation to their ability to diagnose and teach technique. In fact, the opposite is possibly more likely to be true. Why? Because it's likely a truly advanced pianist developed their technique when they were young children. By the time they reach adulthood they very well may forget or discount the work it took to develop their fingers. They also won't know what it feels like for a student who has not had proper early training to play. Additionally, the norm for many advanced teachers is to focus on interpretation and spot-technical problems, not diagnosing and re-building, if necessary, one's basic technique. (not one of the many teachers I've studied with ever bothered to test the power and independence of each of my fingers - alarm - alarm - alarm....). Rebuilding a technique may, in fact, require abandoning repertoire for extended time - perhaps even years. Not many advanced teachers are likely to want to do that.