It can work, provided the staffing company is genuinely her employer and controls her work. The arrangement fails if she is effectively self-employed or if no entity is clearly the employer.
The employer of record must be identifiable and must actually employ
TN requires prearranged professional employment with a United States employer, and the classification does not authorise self-employment. A contract therapy company that hires the therapist as an employee, pays her, supervises her clinically and assigns her to client facilities can be that employer, and the facilities are then customers rather than employers. Two variants cause difficulty.
The first is an independent contractor engagement, in which the therapist invoices for services; that is not employment and TN does not cover it. The second is a structure where the therapist is nominally employed by an entity that exercises no real control, while the facility directs everything, which invites the question who the actual employer is. Ask for the employment agreement and the placement contract, read them together, and if they conflict, get that resolved before an application rather than at a border.