I think that psychological problems and frustrations often arise not because we have faulty core values but because our goals and especially actions are not aligned with them. I certainly had periods in my life when I felt the most miserable due to such dissonance between my values and my life. I also had a therapist who seems to have his core values right and says all the right things about therapy, but the way he conducts it is often the polar opposite in very obvious and annoying ways. My personal opinion is that it is important to figure out our core values if we want to be self aware, but the goal of self-improvement is better focused on achieving a better alignment, not changing the values. My last T actually had this in the center of his therapeutic philosophy in theory (puts on his website etc), but he really did not do much in that area with me even though it was clear that I had the same interest.

Perhaps if someone has issues around their basic value system, I think it is more often a lack of awareness of it and not that it is "faulty".