OK. When I started nursing school, we got a "to do" list of labs and vaccines. It included titers, and then the vaccines if necessary.
Showing proof of an MMR from 23 years ago doesn't really mean anything. I had to get it 3 times before I finally tested immune. Sometimes you just lose the immunity and re-vavvination is necessary. That's why my school stressed that the titers be done.
But if your school simply wants one or the other, I agree with the others... just go get the vaccine. Quick and easy, and pretty cheap too. I got alot of my vaccines, believe it or not, through the "shots-for-tots-" program here. Free, donations accepted.