Ideally, robots used for motor rehabilitation, in particular, during assessment, should minimally perturb the voluntary movements of a subject. In this paper, we show how a state-of-the-art back-drivable robot, i.e., a robot that can be moved by the user with a low perceived mechanical impedance, when used for assessment can still perturb the voluntary movements of a subject. In particular, we show that, despite its low mechanical impedance, a robot may still not comply with the intrinsic kinematic constraints, which are of neural origin and are adopted by the human brain to solve redundancy in motor tasks. Specifically, the redundant task under consideration is the 2-D pointing task, which is performed by a subject with the sole use of the wrist [3 degree of freedom (DOF) kinematics]. Wrist orientations during pointing tasks are assessed in two different scenarios. In the first experiment, a lightweight handheld device is used, which introduces no loading effect. In the second experiment, similar pointing tasks are performed with the subject interacting with a state-of-the-art robot for wrist rehabilitation. In the first case, intrinsic kinematic constraints arise as 2-D surfaces embedded in the 3-D space of wrist configuration. Such surfaces are typically subject-dependent and reveal personal motor strategies. In the second case, a strong influence of the robot is remarked. In particular, 2-D surfaces still arise but are similar for all subjects and are referable to a mechanical origin (excessive loading by the robot). The assessment approach described in this paper, including both the experimental apparatus and data-analysis method, can be used as a test for the degree of back-drivability of mechanisms and robots in relation to constraints of neural origin, thus allowing the design of robots that can actually cope with such constraints. The clinical potential impact is also discussed.