Mayo policy for Medicare patients varied by location in past. Based on Mayo insurance web page, that appears to have changed.

Even though Mayo except Medicare, there are certain specialty sections that might be closed to new patients. And if you have supplemental Medicare insurance, you need to check with you insurance company to see if Mayo is in network.
And like all places that accept Medicare, there are some restrictions on certain tests and preventive care.

I am on Medicare and have a Blue Cross plan that has Rochester Mayo as an in network provider. I have ran into problems with some visits based on how coded, example if coded as routine visit, Medicare would not cover and if Medicare denied, by Blue Cross insurance also denied.

Also, not all tests a provider orders may be covered, but that is not unique to Mayo. If a dr orders a blood test not covered, they will ask you to sign a form before receiving test stating you are responsible for any tests not covered by insurance.

I suggest you check out Mayo Insurance web site, and if any doubt, call and verify info with Mayo and your insurance company before visiting so you have no surprises.
https://www.mayoclinic.org/patient-visitor-guide/billing-insurance/insurance
Laurie