It depends on who is doing the training. And what their definition is of a "swim thru". Agency standards say NO overheads for OW divers. Taken literally that means no swim thrus as you do have something over your head. My definition has changed over the years due to wreck penetrations and most decidedly Ice class. I did a bunch of stuff in the keys on the Spiegel Grove and the Duane, some in the St Lawrence, as well as Lake Erie. Today my definition is if you can't pass two divers thru side by side in proper buddy position, it's more than a body length, and you need to touch the sides, top, or bottom then OW divers should not be in there. I have seen too many people in situations where they had no idea of the risk they were taking. All because someone who met them maybe the day before or that day was shown a card that says they know how to dive took them into a place with the potential to kill.
The absolute worse thing in my mind is a DM, guide, or instructor who has not dived with someone telling them "you'll be fine we do this all the time". That blind obedience to a pseudo authority figure has killed people in Mexico and Italy. The new diver who looks at one of these "pros" an authority on them is a dangerous person. The "pro" did not train them, doesn't know their real skill level or comfort threshold, and yet is going to be trusted so blindly. That to me is a deficiency in their training that they would look at the "pro" in such a way.
I tell my students to never trust anyone to keep them safe. And never accept without question anything that makes them the slightest bit uncomfortable or makes them question their training in any way. Even if it comes from me. When I train them I tell them no overheads. Then on checkouts I'll test them. I'll motion for them to join me under a platform or in a large opening in one of the quarries where there are boats, airplanes, semi trailers, and a silo. If they do it, they fail. I have yet to have one do it as I do my best to impress upon them that no overheads means no overheads. For an instructor to tell students no overheads and then lead them through a place where they can only pass single file and if someone gets in a bit of trouble the rest are stuck waiting til that person is taken care before they can make a direct ascent is reckless, irresponsible, and dangerous.
That is my view and the way I teach. I see no reason to do otherwise.