Any dive center that doesn’t recognize BSAC, or any other certification from a reputable organization is either trying to upsell training courses you don’t need, or has received and is following bad advice from their attorney or insurance broker. I’d just skip that operator as there are plenty of others who will gladly accept your business. :)
You really can’t go wrong with any operators in the Keys as long as the prices and schedules fit your budget. At least, I haven’t had anything I’d call a bad experience yet although Dive Key West did "require" me to wear a snorkel when I didn’t want to and dropped us on a pretty boring section of reef.