Actually, you are pretty much all correct in one way or another.
Holding officers used to fly with AEFs a long time ago. Then the rules changed such that you had to have held and retained Service wings and have at least 500 hours first pilot to qualify to fly cadets.
The holds got longer and there were more people in the system and so pragmatism came to the rescue of common sense and holding officers were allowed to hold with AEFs and fly cadets if they had gained a high average grade on their "wings" course. They also have to be approved by Gp Capt Flying Training (unless his post title has changed again) and also by OC 1 EFTS.
There was (and still is) one person flying cadets who did not have military wings. He is the exception that proves the rule, and I am unaware of any new plans to relax the requirements. If I hear of any changes I'll let you know.