This is the rough reality for many adult students who will be approaching a teacher, and how it gives impressions at a first meeting.
The student has first taught himself, probably using a method book like Alfreds, probably the adult edition. So the student has not been guided in his first steps under observation of a teacher, which means that whatever physical habits were formed are now entrenched. At the same time, since these books do give guidance, it can all look "sort of right" but maybe strangely tense or awkward or something - but maybe not that bad. The student will sound somewhat knowledgeable, because those facts are in the books too. We don't know how the student actually practices and approaches pieces.
If you get a young transfer students who was decently taught, then if you listen to samples of repertoire, you will get "what level the student is at" and can continue on that level. The unspoken part is that this student has also gotten the foundations of how to practice (ideally), the physical etc. As well, because young students are still forming their physical skills, his skills were probably developed in a more basic and less intellectual rudimentary way. None of these things may be there for your adult student who is playing "at level X" (repertoire).
From what I'm reading in forums, there seem to be two general things that happen with adult students. One is an "easy music" approach, maybe just taking whatever favorite pieces and teaching them one by one, maybe doing common chords and melody, etc. The other is where the student tries to be serious and gets a serious teacher with lots of credentials, and the teacher there is used to teaching well trained students and working on repertoire. These teachers may not have any idea on how to actually shape skills. So we get the abusive comments and expressions of impatience.
I may be wrong, but I believe strongly in the foundations that a beginner should get, and that even if a student plays advanced material, these still need to be there. The lack of foundations can also be masked. If a student plays an intermediate piece for you, do you know whether it's been memorized? Whether it took months to learn by playing it over from beginning to end? If a student talks about chords and intervals, is it only intellectual knowledge? How is this student working, and what does he actually know? If he plays a grade 4 piece convincingly, will you think that something commonly taught in grade 1 might be needed?
That is, an experienced teacher may be able to spot things. For example, if a student plays a piece she has learned, and it gets progressively weaker, that may be a sign of poor practice habits - the beginning-to-end kind. Or being given a lower level unfamiliar piece, and not being able to read it at all.