Robotic technologies for rehabilitating motor impairments from neurological injuries have been the focus of intensive research and capital investment for more than 30 years. However, these devices have failed to convincingly demonstrate greater restoration of patient function compared to conventional therapy. Nevertheless, robots have value in reducing the manual effort required for physical therapists to provide high-intensity, high-dose interventions. In most robotic systems, therapists remain outside the control loop to act as high-level supervisors, selecting and initiating robot control algorithms to achieve a therapeutic goal. The low-level physical interactions between the robot and the patient are handled by adaptive algorithms that can provide progressive therapy. In this perspective, we examine the physical therapist's role in the control of rehabilitation robotics and whether embedding therapists in lower-level robot control loops could enhance rehabilitation outcomes. We discuss how the features of many automated robotic systems, which can provide repeatable patterns of physical interaction, may work against the goal of driving neuroplastic changes that promote retention and generalization of sensorimotor learning in patients. We highlight the benefits and limitations of letting therapists physically interact with patients through online control of robotic rehabilitation systems, and explore the concept of trust in human-robot interaction as it applies to patient-robot-therapist relationships. We conclude by highlighting several open questions to guide the future of therapist-in-the-loop rehabilitation robotics, including how much control to give therapists and possible approaches for having the robotic system learn from therapist-patient interactions.