I did use cap gap very first year it was provisioned and renew licenses. My school issued I-20 to cover cap gap gates and savis got extended. I used that I-20 to renew driving licenses and I got license for 3-4 month :). Back then they didn't have automated system, so that used to look at i-20 and issue license upto expirey date of I-20. But again it used to be different in different states. But all school can do is issue I-20 and extend savis, so make sure ur school did it for you.

After that it is dmv. I don't know how dmv does cross check, but you can ask them. Even though system through error , it could be override. Talk to their supervisors, and ask them why can't you get driving license when you have all required document. Hard dodument always overrides automated systems in govt business.