Embodiments of a Wearable Cardiac Defibrillator (WCD) system include a measurement circuit that can render a physiological input from the patient (82). Such WCD systems may also receive a motion detection input that reveals whether a motion event has been detected by a motion detector. Optionally, a value becomes assigned to a motion level parameter in response to whether a motion event was detected or not, and the rhythm analysis can be based on the physiological input and on the assigned value. Optionally, a rhythm analysis of the physiological input may be performed in different manners, depending on whether or not a motion event has been detected. Optionally, a different shock/no shock criterion may be applied to the rhythm analysis, depending on whether or not a motion event has been detected. The patient (82) may receive an electrical shock (111) according to a shock/no shock determination.