I do not know how NLP is taught right know, however I'll explain how I come to that conclusion with a reference to the mentioned book from steve andreas.
One of the basic tools of NLP is what is called "anchoring". An anchor is an association in terms of action->response. One example lots of people can associate with is: You hear a song and have instantly a mood change. You could feel very happy, because you remember meeting your spouse for the first time when this song was played. Or maybe you feel bad because something bad happened when you heared that song and associate the bad feelings with that song.
One way to break away from a specific "action->response" pair is by using a pattern interrupt and overwriting the usual response with another response. You do that regularly yourself, for example when you learned a false fact and correct it afterwards.
Of course you can also create new associations. You probably do not have any strong feelings associated with a song when hearing it for the very first time, but you can associate something with it.
Anchoring, pattern interupts and overwriting old anchors is heavily used in behavioral therapy, and is also the basic concept for a lot methods in NLP.
For me the parallels to behavioural therapy are why I conclude "generally do work".
I think the bad reputation NLP is receiving is because of "hype-riders", people who want to rip the help-seeking people off their money. And as you do not have to study psychology to practice NLP (or say you can do NLP), charlatants have an easy entry.
In Steve Andreas book, you learn how to rewrite old anchors effectiveley, specifically the ones that make up your identity, the "how you know you are you".
Example Scenario:
Current situation: Suppose you think you are bad at maths and that is simply your personality, that's why you will never solve any math problem in reasonable time.
Effect: You will not even try to solve math problems or will not have fun doing it, thus taking more time or limiting yourself in other areas as well as panicing as soon as you see a math problem.
How you change that? ->
1) Think about how you know you are bad at maths.
2) Do you imagine one or multiple situations where you were bad at maths? Are these pictures or video? How are they organized in your head? In color or black/white? Big/small?
3) Now take every example in your head that support that belief and change the modalities. Already at that point you will notice with each transformed example, that you feel less bad about maths.
4) Next you build positive images around maths in the same way as before, thinking about situations where you were good at maths and transform your images to the same modalities the bad images were before.
5) Pro step: Build values for yourself such as: intelligent, resilient, motivated and associate these values with situations were they helped you in solving math problems or other problems. This would decouple your identity from "maths" and help you not fall into panic as soon as you encounter a math problem or any other problem you think you are not good at (remember, you are intelligent, resilient and motivated?)
I do not know if specifically this technique with exactly these steps is used in todays scientific therapy. However, it is based on anchoring/overwriting old anchors and I do not see much novelty there.