YA states that it is a matter of not authorizing yoga instructors to diagnose or treat medical problems. However, the benefits of yoga are so holistic, that the yoga instructor community that is dedicated to the promotion of well being and support for special populations that require modifications and special focus in a yoga class is frustrated by the lack of being able to list their skills and training as having these positive results/applications. Moreover, they are at risk for having their YA membership and certifications revoked if they do even so much as list the word "heal" on their YA profile (case in point: I had written that I started doing yoga to help heal my mind and body after mental and physical illness. I had to remove the word heal under threat of losing my certification). While there are special designations for Prenatal Yoga and Children's Yoga, there aren't ones for Chair Yoga, or Yoga for Multiple Sclerosis, or Yoga Therapy under the umbrella of the Yoga Alliance. Of course people can train and earn completion certificates from whomever they want, but they won't carry that special "YA" accreditation; there is something valuable about being recognized from a central "authority" with universal standards by which employers and students can gauge their instructors (not unlike the value of bachelor or master degrees from colleges/universities).
All that being said, there is a plethora of excellent work being done out there, whether "certified" or not by Yoga Alliance, by highly qualified, highly educated, highly practiced yogis who are also doctors, scientists, therapists, teachers and other health and well-being professionals.
For example, there has been amazing research on yoga for PTSD by Bessel Van Der Kolk., M.D. who wrote The Body Keeps the Score (my current read that is getting road-worn because I drag it everywhere so I can turn a page any time I have 10 seconds free). On Dr. van der Kolk's website there is an article in which he was interviewed by Integral Yoga Magazine. He said
My interest came from doing research that discovered how trauma affects the brain. Yoga turned out to be a way to get people to safely feel their physical sensations and to develop a quiet practice of stillness.Here, have a read:
In the meantime, it seems to be very much about semantics, so I can promote myself as a yoga teacher and you and I can just know what's happening inside might be considered (insert the T word here) but we'll just say we had a good practice!