I can't keep track of who told you what.
If it's Dover Rehab, they might not be aware that Tom's doctor 'ordered' the stay in the nursing home.

From the site SINSULL linked to:

As long as it is medically necessary, Medicare will pay the full cost of the first 20 days and part of the cost of another 80 days of care in a Medicare-certified skilled nursing facility (SNF) each benefit period. A benefit period begins the day you enter the SNF and ends when you no longer receive SNF care for 60 days in a row.

The co-pay bullshit is bullshit.

There HAS to be some mis-communication. Maybe the facility is afraid Medicare won't pay or they think it's his choice. In the end, I think Medicare will pay. From everything I've read, they'll pay and are putting you through because they're the idiots who got stuck working on a holiday and your doctor isn't around. I think when tomorrow rolls around and Tom's doctor is available (hopefully), this will come to an un-natural concentration of stupid in a small space/time.

QUESTIONS:
Medicare. The federal government has a toll-free number (800-MEDICARE) and a web site (www.medicare.gov) to help you get basic information about Medicare coverage and your private health plan options.

The State Health Insurance Assistance Program, or SHIP, is a national program that offers one-on-one counseling and assistance to people with Medicare and their families.