I was trained to dive at a university and taught at few also one of them was a graduate school for oceanography. In all cases the students had to use the university supplied equipment nothing else or, in the graduate school for oceanography, had to buy their own equipment based on a very specific and defined list of what is acceptable to use in the school's program with no variations were accepted at all. In all cases the programs had a specific way of doing things with specific equipment at a specific standard.
I don't find any fault with this dive shop's requirements and it isn't an exception at all.
That's interesting, as my experience (as undergraduate and grad school diver and now DSO/instructor in a university setting) is the opposite. The marine labs I did my work from had tanks one could use, and one had a fair collection of lead. But the expectation was you had gear of your own, either belonging to you personally or to your PI's lab. If I had to hazard a guess, I'd say most folks had their own gear so they could dive for fun as well as at work. Same where I am now: We require receipts showing (e.g.) annual maintenance or purchase within the last year but divers have their own gear. (Again, excepting tanks, etc.) There's no AAUS requirement that only university-provided gear be used.
I'm very skeptical on the whole liability angle on this. I live in Washington State which I don't think has substantial limits on jury awards relative to Alabama. My LDS includes gear use (OW and pool, but different gear) in the price as do I think most of the local shops, for OW courses. However, from AOW on you either own your own gear or rent from them. They don't care which, they don't check maintenance history, nothin'.
If there's an equipment liability angle on this, it'd have to be very specific to an Open Water class and magically disappear once you get certified. (And even in OW to my knowledge a student could dive in their own gear with my LDS, though it won't get them a price break.)
Let's just assume liability magically disappears at certification, as it must if advanced courses and guided dives from tropical DM's don't seem to require you use their equipment. It seems to me that the key piece of education that differentiates here is classroom based, not skill based. OW classes don't teach you anything about maintenance in the "skills" requirements, just in the "book-learning." Why wouldn't completing the book-learning make you as qualified to judge your gear as finishing the certification?
Now I can sympathize with the shop charging a steep rental fee: It basically becomes a discount on course cost if you buy gear from them. Maybe that attracts some folks. I always wondered why my own LDS didn't add the cost of dry suit rental to the cost of a dry suit course, and discount if a student bought a dry suit from them. (Every student I've certified DS has rented. I did have one who bought first but wasn't physically fit enough to walk down the beach in heavy gear so didn't get certified.....)