The ones who seem threatened by it seem to want to embrace and perpetuate the 'mystery' -
I've seen a lot of this too. Ironically, even from people who could really play. And when people who can "really" play (or who, in the eyes of an inexperienced musician, seem to be an authority on playing) perpetuate that music is all a "mystery", I think this type of misinformation can be misleading and outright damaging!
When I was in high school, I was in the "jazz" band. (I put "jazz" in quotes, because my walking bass lines were written out note for note, and there was absolutely no discussion of theory in the class.) Anyway, I innocently asked the teacher, who played saxophone, "What kinds of scales/approach do you use when soloing?" I basically got a frown with a disapproving comment like, "That's not how it works. You should just be feeling it." Jazz just became even more daunting, and all I could think was, "Well, hopefully, one day, the light bulb would come on... I'm still in high school, so I'll figure it out one day."
Many years later, I took private lessons from an upright player who doubled on bass guitar. We would just go over standards, but there would be no discussion of what to play. No written examples of lines that work over common chord progressions, which was really what I wanted to work on. (In fact, I now realize that it should have been the teacher's responsiblity to find my areas of weakness and address them, instead of me trying to figure out how what I needed.) Anyway, we would take turns trading solos. I would listen to his playing, and when I heard something that sounded "cool", I would stop him and ask him what he did. He explained for example, how playing #9's and b9's over dominant 7 chords could sound good if you resolve them. But the more I tried to pick his brain, I was also met with a response like, "You are thinking too mathematically. You shouldn't be doing this etc. You should just be hearing and feeling them. etc etc"
I remember feeling kind of dejected by this "mystification" that was being perpetuated. I knew I was improving from all the self-study, and analysis that I was doing on my own time. But I felt like I was walking in the dark at times and if "accomplished players" couldn't teach me, then maybe I would never be capable of playing jazz.
Fortunately, I have since come across good resources in books and materials written for piano/horns. These materials really contain a lot of analysis of lines that are academically sound. And it enabled me to see that the academics of the actual music and jazz licks (and not just the theory) can also be systematically taught.
Anyway, my rant is getting long, but the point I wanted to make is that IMO, bad musical advice and "jam buddy lessons" without real musical content can be damaging to trusting students.