They don't take insurance so I'm not sure about cms involvement. And to that point, I notice alot of therapists employ students.
Here there are groups. Usually 2 psychologists, 2 ma, 2 students
There are a good deal of professionals who function like this; at least from my experience, the way this is set up is like this:
1. Master's level practitioners function as technicians (i.e., they administer the neuropsych tests and depending on their education and experience, will also score and write up results). After the tests have been completed by the technician, the neuropsychologist must be the official person who has the last review and will check their work before meeting with the patient to discuss results. Also, when using a technician, the supervising neuropsychologist will bill the insurance under the code for "technician" vs. "psychologist."
2. When a private practice is using students, they are graduate students (most of the time doctoral students, sometimes master's level students). Their exposure to patients and testing are typically on par of a technician, but a lot of their time might be spent doing biopsychosocial intakes and other tasks before getting into more intense activities such as administering full neuropsych batteries.
Either way, technicians and students are supervised by a neuropsychologist who often times provide training on the job or, they are providing supplemental exposure to psychometric testing, structured interviewing, etc. that is essential for developing student neuropsychologists. Technicians are a great way for a private practice to take on more patients to expand revenue since the neuropsychologist is more free to write up opinions, results and to spend more time with the patient to discuss those results.
Neuropsychologists are a mixed bunch; many bill insurance and many are moving away from that. The private practice I worked at billed insurance (medicare and medicaid were more profitable in most cases). Several private insurance companies may not pay the full cost of neuropsych. testing, so this is a reason why several neuropsychologists might be dissuaded from using them. There is a very successful neuropsychology practice in Miami (he actually has two locations now) who enjoys pediatric neuropsychological testing since most of the tests are paid for out of pocket by the parent(s), so he is able to be more profitable in terms of return on investment (adult vs. pediatric testing).