Your still going on about nonsense. There is no agency that doesn't recommend training before diving in an overhead.
I don't know of any agency that says you must have training before you go into ANY overhead. I will give details for PADI, since that is one of the agencies for which I instruct and it is the one I know best. Here is what I know:
1. In a recent thread in which other PADI instructors with full access to all standards argued that the agency forbids all overheads, these instructors tried hard, but they were not able to find any such standard.
2. The closest they could find is one of the statements in the safe diving practices document that specifically states training is required for
cave diving. No argument here, but that is not ALL overheads.
3. PADI has a standard for instructors saying that they cannot take students into overheads, with the exception of courses that teach overhead diving and
local orientation dives. Local orientation dives introduce divers new to the area to local dive sites they may later wish to visit on their own. This standard clearly assumes those divers will want to access those overheads on their own after being led there by an instructor. I witnessed one such local orientation dive in March in which the instructor took customers into a small wreck.
4. PADI has an officially approved distinctive specialty that teaches students to differentiate between overhead environments that can be dived without further training and those that demand further training. This clearly indicates that PADI has no such policy against this, since it would not approve a course that violates its own policy.
5. PADI 5 Star facilities are required to adhere to PADI policies. Hundreds of PADI 5 Star facilities around the world feature entry into overheads as part of what they offer for divers.
So, all of that indicates that PADI does not have a standard that tells divers that they cannot enter simple overheads. Please note that to refute this, all you have to do is identify one statement from PADI that says that it does not allow its divers to enter ANY overhead without training for it.