Frustrating Medicare catch: Who's an in-patient at the hospital and who's under observation?

Frustrating Medicare catch: Who's an in-patient at the hospital and who's under observation? | Fox News:
"But when she was 95, Felton fell late one night at home and was taken by ambulance to the emergency room, where doctors found she'd broken her pelvis in three places.

Brier said the doctors told her that after leaving the hospital, her mother "would have to go to rehab and learn to walk again and learn to function again."

But Brier and her sisters were told that would mean a skilled nursing facility, which is expensive. But, if she "stayed three full nights, we were told that was the criteria for having Medicare pay for the rehab," Brier said.

There's a nasty catch, however-- many people in the hospital are not officially considered "in-patients" but rather "under observation" although the difference is not obvious.

Says Toby Edelman of the Center for Medicare Advocacy, “Once they are in the hospital and in a bed for several days, getting care and treatment and medicine and food, (a) wristband, they think they're in-patients.  People have no idea that they're out-patients.""