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.
Hi John. I have to take exception to this. From the 2010 PADI Open Water Diver Manual on page 139 there is an entire page devoted to Overhead Environments. In particular I quote "For this reason, until you have the training and equipment you need do not enter a cavern, cave, wreck, or any other overhead environment. Doing so places you in an unnecessary and extremely hazardous situation." [italics are PADI's].
PADI goes on to say that anytime you cannot directly ascend to the surface you are in an overhead environment. Therefore the Mexican cavern and the wreck qualify as overhead environments. Swim-throughs share the overhead but with one important difference: a diver can ascend immediately and while swimming forward exit the overhead. The arches in Cozumel qualify as excellent swim-throughs. The Devil's Throat on the other hand does not qualify, as it is a fairly small (a restriction - two divers cannot enter side-by-side) coral tunnel about 50 ft long. The cavern and the wreck require a significant (to an untrained rec diver) lateral swim before ascending.
Please forgive me if this point was mentioned later in this thread. I didn't read the thread all the way through.