When you say physical portion of the exam do you mean the physical test, which does not contain any of your answers?

Also, despite what your professor has said about receiving a C+, what grade does your school curve to? If it's not far off from your median, than maybe you just a didn't do well. Did you feel like you knew material as well as in your other courses?

On one hand, I don't see a school failing a student because they couldn't identify your physical exam packet. Assuming you were the only student to forget to put your ID, the extra exam could easily be identified as yours.

On the other hand, I have heard of some pretty fucked rules at other law schools. That, coupled with receiving high grades in your other classes could mean your grade was lowered for some reason.

I know at my school we only need to put our BAGS number on the physical exam because leaving with the exam is an honor code violation for some reason. Kinda of a dumb reason since all the professor's release all of their old exams though.