How does one know if they're vaccinated or not? Who has a complete medical transcript going back to their childhood? How do they even get the vaccination rate data? I call BS.
We're really bad about centralized health data in the US, but schools keep track of immunization data. How long they retain your records will no doubt vary.
Ask your doctor. If it isn’t in your records, an antibody titer blood test is definitive. For public health purposes, these data have been collected for a long time.
Plus in some places (like California) you can get a free MMR vaccine at pharmacies like CVS, without making a doctor appointment.
ADDED: So, no, as someone born 1960ish I would probably have to get a test to prove I was vaccinated against all the standard diseases.