Yes Mayo clinic does just that with medicare unless you are one of its retirees or volunteers.
Only a few hospitals in the US don't except Medicare, primarily VA hospitals and Shriners. The reason why is pretty simple.
60% of the hospitals are nonprofit hospitals, many of which depend on endowments and government grants. With approximate 1/3 of the hospital beds in the US being occupied by Medicare patients, turning down Medicare is simply not an option for most hospitals particular when you consider that about 40% of the people covered by Medicare have other insurance in addition to Medicare which will cover almost all of their hospital bill not paid by Medicare.
Many hospitals are faced with cuts in Medicare reimbursements if they don't improve their outcomes measured by readmission within 30 days and a number of other criteria. For hospitals that excel, their reimbursement rate will increase. Most hospitals will improve their patient outcomes rather drop Medicare.
BTW Mayo Clinic does accept Medicare. However, it doesn't accept Medicare-approved payment amount as full payment of physician services. On a $1150 bill, the patients responsibility is likely to be $150.
Medicare information for Mayo Clinic in Arizona