My instructor could hand out any card he wanted upon request. While an SSI shop, I requested a NAUI card. Could have provided a YMCA, La Country, NAUI, PADI, SSI, and Harvard mail order degree if I wanted. All my subsequent training mostly has been NAUI. Actually, after completing LACO ADP I also got a NAUI rescue and master diver with it. What's it matter?
There are some places I've observed produce really crappy OW students and some that produce spectacular students. It is the instructor, not the shop (for the most part). The best thing to do is hopefully find a good diver and ask them where they got their training (if locally) and accept the referral. Talk to the instructor first and determine if you even like them and so on, but the fact is a pre-OW is in no position to adequately interview a potential instructor for qualification. Sometimes you just take roll dice and take a chance. Every instructor will get you in the water so you can fill tanks and most hopefully safely.
I was at Catalina Island today and 3 rescue crews were called to the Point because of students panicing or doing becoming endangered in some way. I thought to myself, how the hell can our state of training be so bad that thrice in one day something happens during training? This is only the day I'm there, what about others?
Over time, I'll be you that students of such incidents will have come from SSI, PADI, NAUI, YMCA, SEI, or whatever. If students follow their training from most any instructor (not all instructors), they will probably be fine. 3 simple rules: Respect your training limits, watch your air, don't cork (and if you do don't hold your breath). Such is taught in all OW classes. Just some instructors are better about not granting a card until the student is ready.