Welcome! Thank you for your question.
The facility is nearly certainly incorrect. Your mother, if she is mentally competent, or her appointed attorney in fact if she is not competent has the right to leave the facility regardless of whether the doctor or facility agrees to discharge. It is very rare that this would have an affect on Medicare paying for the services already provided.
Medicare covers a medically necessary inpatient rehab stay, as determined by the doctor who "admits" you to the hospital and by the rehab staff's continuing certification that it is necessary. Medicare, too, must agree that the stay is medically necessary. But the days of your stay would not retroactively become medically "unnecessary" just because you check yourself out before your doctor officially discharges you. If your stay in the rehab was appropriate in the first place, under Medicare rules, that stay should be covered regardless of the circumstances of your discharge.
There are a few circumstances in which a medical service might not be covered if a patient interrupts the care being provided. For example, if someone is undergoing physical testing or screening but leaves before it is completed, the office or clinic providing the care might bill the patient for the service but Medicare would refuse to pay its share of the bill. Or, if a patient is undergoing a treatment that must be completed in several stages but fails, without good reason, to complete the treatment, Medicare might refuse to pay its share of the bill. Unless some similar circumstance occurred regarding your stay, Medicare would have covered your inpatient care regardless of whether you waited for your doctor to discharge you.
Here is a link to the long term care ombudsmen program for the state of Michigan. They provide free patient advocacy and will assure that your mother is heard and given her proper rights with regard to treatment. Contact your local ombudsmen and get them involved.
I cannot provide you with legal advise. I have provided you with information about the law related to your question. My answer, and any information that you find online, should not take the place of having a consultation with a lawyer in your area to advise you regarding your specific issues.
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