Thousands of Medicare enrollees in Massachusetts and across the country are finding themselves caught in the same perplexing bind: Despite long hospital stays, they have been deemed observation patients or outpatients whose follow-up care is not covered. They also can face higher costs for the hospital stay itself when they are not officially admitted. These observation patients usually share rooms with regular inpatients and receive care from the same doctors and nurses, making their status invisible to them. Hospitals say it's not their fault. Executives at Beth Israel Deaconess and other institutions say they are just trying to follow Medicare billing rules that even they don't always fully understand. [Registration required.]