@msgolfnut

It may depend on type of Medicare insurance and location. Medicare coverage can be confusing, there are so many types of Medicare plans.

Few facts on Medicare and Mayo. Each Mayo locations has different policies on insurance they take. So Rochester, AZ and FL differ on if accept original Medicare or Medicare Advantage policies, so you need to check with location your considering and your mom's insurance policy.

Mayo's page on insurance has more info but does not provide enough detail to answer your questions, it is vague on on what each location will accept:
https://www.mayoclinic.org/patient-visitor-guide/billing-insurance/insurance
I am not as familiar about referrals and insurance. If the Mayo location does not take your mom's insurance (you're not in network) sometimes the insurance company make exceptions if provider refers the patient to a specialist that the in-network clinic can not provide.

When you call to make an appointment at Mayo, they will ask about insurance and advice you. If the location does not take your mom's insurance, you can ask if provider does the referral if makes difference.

If your mom has a Medicare Advantage plan, you can call the insurance company ask those questions.

How are you doing being caretaker and having to handle all this?
I was primary person when my mom was sick, and it takes a toll. Make sure your taking care of yourself.