Most people are surprised to learn that PADI does not say in any of its materials that divers are not supposed to enter ANY over head environment. Individual instructors may well say that, and I am sure many do, but PADI does not.
My OW manual, under heading of "A deceptively easy way to die" says: "Do not enter a cavern, cave, wreck or
any other overhead environment unless you have the training and equipment you need".
On the literal reading of those words, swim-throughs should not be entered. Personally, I have entered plenty of swim-throughs (always shallow, wide and supervised by an instructor). I would not enter a wreck at 30m depth, but it is difficult to know what is and what is not ok and where the cutoff point lies - especially when you are not experienced enough to know what you don't know.
There's even more potential for confusion when reputable dive ops appear to allow or encourage unqualified overhead diving. When looking for some diving opportunities to combine with a holiday, I was shocked to see that, at least one dive op allows "unlimited penetration" of a wreck at "all depths" for AOW certified divers, if accompanied by a guide. The wreck in question is at a little under 30m deep. This is in Queensland, Australia, where one would hope safety would be top notch.
Having done a wreck dive as part of AOW certification, the most useful thing I learned was to
not penetrate the wreck without further training.
But there are too many mixed messages and little consistency between training and practice.