Smarter outfits require seeing a logbook with so many dives, and to see what type of dives have been done. For example, if it's a more advanced deep dive, they might check through your logbook to make sure you've been beyond 60 feet a few times before they let you go down to 120 feet.
I don't think it's a common practice though unless it's for a somewhat specialized or difficult dive. Browsing this forum you'll find how meaningless an AOW card really is... so some dive OPs will require a logbook with a certain number of logged dives instead of some card with some crap printed on it saying you're ok to do it.
Plenty of places let anyone on board though becuase they are recreational dives, and not really pushing the limits on anything. Just becuase it's the same location, doesn't mean it's the same dive. You might goto 30 feet in the daytime, they might goto 100 feet at night. Or they simply might not be equiped to handle new divers and find that going with more experienced ones make things generally run alot smoother?