Why would a recruiter ask for my old drill sergeant's full name and rank?

I don't know. However, I would comply with your recruiter.

Maybe to get the low down on how the RE code was put on you for your request of waiver?

Do you want to come back in or not? What about the fact that the recruiter must waste man hours on putting together a waiver for you? Have some discipline and appreciation for the work he/she is doing for you, because let me tell you something high speed, a waiver is a distraction and time consuming process that takes the recruiter away from finding quality qualified applicants for the Army. Good luck in your future endeavors.