I'm doing my PM&R rotation right now. It's tough to describe in one sentence what exactly a Physiatrist does. And a lot of guides out there are pretty worthless in their description, as they talk in broad terms without discussing specifics.
Basically, there's inpatient rehabilitation and outpatient physical medicine.
When you do inpatient rehabilitation, you are essentially the primary care (Internal Medicine) doctor who rounds on the patient's each morning, and manages their chronic medical conditions and ship them back to the main hospital when they develop new, severe acute conditions. The afternoon is spent discharging and admitting new patients. You meet with physical therapists, occupational therapists, psychologists, social workers, etc. once a week at a treatment team meeting to provide feedback on the patient's medical issues. It is at these meetings that rehab. goals are discussed, and a discharge date is set. There are usually a few different services (which represent some of the main reasons someone would go in for acute rehab. hospitalization in the first place): stroke, traumatic brain injury, spinal cord injury, and general (which includes orthopedic and neurosurgery patients after their procedures, and others who are "deconditioned" from long stays in the hospital). However, they all operate pretty much the same way. Inpatient rehabilitation is very similar to an Internal Medicine or Neurology service (though not nearly as intense in overnight call/patient emergencies and turnover rate), which is why some people dislike it.
Outpatient physiatry will consist of different specialized clinics. A general clinic for example will see patient's previously hospitalized in rehabilitation hospitals and adjust various pain, depression, and neurological medications. A spasticity clinic will involve adjusting the baclofen dosage of patients with severe spasticity from stroke, cerebral palsy, etc. An EMG clinic will involve performing numerous NCV's and EMG's on patient's referred for peripheral nerve conditions like Carpal Tunnel syndrome. A wheelchair clinic will assess patient's problems with their wheelchairs. A TBI clinic will involve managing the neurological issues of patient's who have suffered traumatic brain injury in the past, and are now well past their stay in an acute rehab. hospital. Same with spinal cord injury clinic.
I wasn't aware El Paso had a program. In Texas, Baylor is supposed to be good.
My impression is that these rehabiliation hospitals are quite expensive and are owned by corporations, academic medical centers, or health care groups, who then employ Physiatrists. I'm not sure if outpatient rehabilitation places like you describe even need Physiatrists. Physiatrists do not oversee PT, OT, SLP, etc. The outpatient clinics however are owned by the Physiatrists themselves.
Actually, from what I've seen, at least at the major rehabiliation hospitals the Physiatrists have very little power over the physical therapists, and do not involve themselves excessively in the day to day details of what they do. The PT's have as much, if not more say in how long a patient gets to stay. What is true however is that Physiatrists perform no actual physical therapy themselves. At my institution it would be totally bizarre to see a Physiatrist peform a massage on someone, let alone any kind of physical or occupational therapy. I have however seen Physiatrists assess things like strength and gait on rounds, during which they may hold a patient up themselves.