At first, I thought the OP was unnecessarily alarmed. But I looked at the CDC website, and I saw the expression "presumptive evidence of immunity."
"ACIP recommends that people who don't have presumptive evidence of immunity to measles, mumps, and rubella should get vaccinated against these diseases."
( https://www.cdc.gov/measles/hcp/vaccine-considerations/index.html#cdc_generic_section_2-presumptive-evidence-of-immunity )
The same page suggests that "healthcare facilities should consider vaccinating healthcare personnel born before 1957 who lack laboratory evidence of immunity or laboratory confirmation of disease". In other words, this is about safe management practices, not about personal safety.
This may be another case of highly technical, facility-related, healthcare information causing fear, confusion, and doubt. And it creates fear of possible regulatory surprises while traveling, although I don't think that is the OP's primary concern.)
(I was born in 1951 and remember having Measles, with my sister. I've had seven Covid-19 shots.)