refer again to the flow chart in the Alert Diver Article Alert Diver | Rescue of an Unconscious Diver ;the most controversial process box contains the legend "Head in neutral position -Ascend according to training agency recommendations". As originally taught by GUE and per UTD's current protocol, the go to DIR method that was always promoted as being the best implementation protocol was the Toxing Diver Rescue Technique.
I am not sure I understand the sentences I quoted above. Allow me to repeat what I think you are saying in my own words so you will have a chance to correct my understanding. You quote the flow chart box that says "Head in neutral position--ascend according to training agency recommendations," and then you indicate that the linked technique is the recommendation of GUE and UTD, so it is according to training agency recommendations.
Let's look at the paragraph that introduces and explains what led to that flow chart:
Our team used the Professional Association of Diving Instructors (PADI) Rescue Diver Manual as a starting point for the expected behavior of a rescue diver assisting a victim. Rescues were analyzed and reviewed in three phases: 1. preparation for ascent to the surface, 2. retrieval of the victim to the surface, and 3. procedures for the care of the victim at the surface. Special considerations for victims found with a rebreather were reviewed for each of these phases.
It's pretty clear from that explanation that "training agency recommendations" refers to PADI, not GUE or UTD. Even if the phrase was intended more generically (as in, SSI, SDI, NAUI, etc.), it does not refer directly to the UTD recommendations because in this (and many other situations as well), UTD has non-standard recommendations. If they had wanted you to follow UTD recommendations, that would have been specified, since they differ from what almost all others recommend.