Properties of neural controllers for closed-loop sensorimotor behavior can be inferred with system identification. Under the standard paradigm, the closed-loop system is perturbed (input), measurements are taken (output), and the relationship between input and output reveals features of the system under study. Here we show that under common assumptions made about such systems (e.g. the system implements optimal control with a penalty on mechanical, but not sensory, states) important aspects of the neural controller (its zeros mask the modes of the sensors) remain hidden from standard system identification techniques. Only by perturbing or measuring the closed-loop system "between" the sensor and the control can these features be exposed with closed-loop system identification methods; while uncommon, there exist noninvasive techniques such as galvanic vestibular stimulation that perturb between sensor and controller in this way.