Sure, but it's not quite so simple.
Many people over here have been involved in Kukki TKD since the mid-'70's and hold high KKW certification. They are professionals whose livelihood is TKD. They have been to the ETU-KKW seminars, been to Korea, studied with Korean masters. They feel aggrieved that the KKW has only made a real effort to "correct" them since about 2005. They wonder why the KKW saw fit to effectively give its senior masters abroad free rein to teach whichever Kwan style they liked in the name of KK-TKD for so many years. They prefer the ways they were taught all those years, but now find themselves obliged to teach something they are unconvinced of. Perhaps they should stop claiming to teach TKD, then, shun all KKW/WTF tournaments and gradings, close their gyms or put up a new sign saying "Independent Korean Karate". Or perhaps they should feel no obligation to flush away decades of hard work, good results and an honest job that has provided for their families.
I don't disagree with any of what you're saying. At some point, apparently around 2005, the KKW decided to correct them after years of greater freedom which caused them to be aggrieved. You're getting into organizational politics at this point.
If they don't feel convinced of what they're teaching, then it is up to them to decide whether to continue teaching it anyway or to teach what they feel that they should be teaching. If teaching what they feel that they should be teaching means breaking off from the KKW then in good conscience, perhaps they should. I don't know. It isn't my decision, and for them to do that may severely impact their livelihood, so I imagine that it isn't an easy decision to make.
Whatever the case, if the body of curriculum is labeled "Kukki Taekwondo" and the Kukkiwon has published standards regarding the technical requirements of Kukki Taekwondo, then those are the "correct" standards for that art. There is a reason that it is called Kukki taekwondo rather than Song Mu Kwan, Chang Mu Kwan, Chung Do Kwan, Ji Do Kwan, or Mu Duk Won. Though the KKW came out of the Kwans and though the technical body was signed off on by the kwan heads, it is not kwan era taekwondo (no value judgement). If they were lax in issuing correction, that is a separate issue from what constitutes the KKW standard.
For my part, I don't make a living from the martial arts, haven't been affiliated to any org for years now, and don't use the name TKD for what I teach, even though my peers and students are mostly TKD people and even though I acknowledge that what I do is based on what I thought at the time was KK-TKD.
What you do was passed to you by your instructor and in turn, you pass it to your students. I see nothing wrong with that at all, regardless of what you call it. The fact that you don't call it KKW TKD means that you're not in any way obligated to conform to their standard.
Did I write a book about the patterns of KK-TKD? Yes. Do I consider these patterns valid and use many aspects of them in my own teaching? Yes. Do I claim to teach KK-TKD or the official versions of its patterns? No. Do I feel any obligation to perform the pattern movements using body mechanics that I objectively consider to be inferior to the older more Kwan-influenced body mechanics? Certainly not.
I see no reason for you to feel any obligation to perform the pattern movement using body mechanics that you objectively consider to be inferior to the older more Kwan-influenced body mechanics. You should teach what you feel you should teach and be true to yourself and the art that was passed to you by your sabeom. Names and organizations are superfluous to the quality of what one teaches.