I realize this is a joke, but....A good opportunity for PADI to devise a "35' U-shaped Swim Through Certification".
I had a very long discussion with PADI headquarters a few years ago about (roughly) this topic, only in regard to wreck diving. To summarize the discussion at that time, it turned out that PADI considers a basic swim-through to be open water, not an overhead. I was specifically referred to the 1991, 4th quarter training bulletin that even said it was possible to take OW students through a short swim-through during a certification dive.
Our debate had started with the statement in the wreck course that it was necessary to lay line any time you penetrate the wreck, and I had shown a video of divers cutting the corner of a wide open deck. I was told that was a video of a "Swim-through," not a "penetration." I pointed out that the course doesn't mention swim-throughs, and they said it didn't have to, because everyone knows swim-throughs are open water.
To cut to the end of the story, they accepted my suggested alternate definitions for swim-throughs and penetrations, and they said that my wording would appear in future rewrites of both the wreck and the OW course. They then published my wording in their professional journal a couple years ago.
The difference is huge. Their previous attitude could be summed up as "just say no to all overheads," without every coming out and saying "swim-throughs might be OK." My more extensive wording describes a very basic swim-through accessible to anyone and talks about the complications that might require special training and/or equipment. Instead of "just say no," it's "Use your head--do you have the skill, equipment, and training to do this safely?"