Physicians should bill for patients in  facilities based on the status of the patient in the facility.  This is true for Observation, Inpatient and nursing facility status.  The status billed by the facility and the E/M codes selected and reported by the physician should match.

Some hospitals have beds that they designate as swing beds: the patient can have either inpatient or nursing facility status.  Here is what the Medicare Claims Processing Manual says about this: (Pub 100-04, Chapter 12, Section 30.6.9 D)

 D. Visits to Patients in Swing Beds
If the inpatient care is being billed by the hospital as inpatient hospital care, the hospital
care codes apply.  If the inpatient care is being billed by the hospital as nursing facility
care, then the nursing facility codes apply. 

That is, if the patient is assigned inpatient hospital status, bill with codes 99221--99239.  For subsequent hospital visits, use codes 99231-99233.

If the patient is assigned nursing facility status, bill with nursing facility E/M codes, 99305--99310.  It is not payable to bill a discharge from the hospital and admission to a nursing home for the first day the patient's status changes in a swing bed. Bill only a subsequent visit. This is described later in that section of the manual:

E. Physician Services Involving Transfer From One Hospital to Another; Transfer
Within Facility to Prospective Payment System (PPS) Exempt Unit of Hospital;
Transfer From One Facility to Another Separate Entity Under Same Ownership
and/or Part of Same Complex; or Transfer From One Department to Another
Within Single Facility
 
Physicians may bill both the hospital discharge management code and an initial hospital
care code when the discharge and admission do not occur on the same day if the transfer
is between:
 

• Different hospitals;
• Different facilities under common ownership which do not have merged records;
  or
• Between the acute care hospital and a PPS exempt unit within the same hospital
  when there are no merged records.
   
  In all other transfer circumstances, the physician should bill only the appropriate level of
  subsequent hospital care for the date of transfer.

I have bolded the last sentence of this section, in support of billing only a subsequent service on the date the patient is transferred from inpatient to nursing facility status (swing bed).