Here is my experience with OW lessions. All gear including BC, tanks, computer, regs, wetsuit and hood were part of the price. The only gear required was mask, fins, gloves, and booties. If you had your own gear they were subjected to the approval of the instructor since some of the divers wanted to use snorkel masks. If you bought from the store as a student you were offered a discount. You were encouraged but not required to purchase gear through the store but they also had a price match for internet prices for any of the same brands carried in the store.
I did but several items from the store including a wetsuit, BC, mask, and fins. I also purchased a BC online for my daughter since the rental ones they had for her didn't fit perfectly. She is also very petite at 15 and even the XSM BC they had was still a little loose. I have signed her up for AOW classes and there is no question regarding the BC and they are going to train her even in gear that was not purchased through them. In fact the owners don't care and since they service the same brands in the store (just didn't carry that particular model) are more than happy to service the BC even though I didn't buy from them.
I did look at many other dive shops in town before picking the eventual LDS and instructor. Another store actually told me that even if I purchased elsewhere they would be more than happy to show me how to dive the gear I purchased. I would say that any LDS that tells you they can't give you lessons in gear that was purchased elsewhere is not telling the entire truth. It may be their shop policy but is not an insurance requirement. If a shop owner will bend the truth by telling you it is an insurance requirement imagine how they will treat you or what they will say to you if something goes wrong? How could you ever trust what they say to you after that?
