Ok. Now it's becoming clearer.
This just got immeasurably more difficult.
Your only argument at this point is:
You had no reason to believe the registrar did not have the authority to override the department chair. If you had reason to believe the registrar had such authority then you argue they made the call and rescinding it now causes irreparable harm
If you had any reason to believe the department had the final say, it's real simple: you lose
With that said, any time I have attended college or university it was clear the degree was awarded by the college/school (for understanding sake: the department) and not the administration or university. A school or college is generally considered an independent entity within a university. The general university adminstration is, for lack of a better definition, the coordinators of the schools within the university.