The era of AI-based decision-making fast approaches, and anxiety is mounting about when, and why, we should keep “humans in the loop” (“HITL”). Thus far, commentary has focused primarily on two questions: whether, and when, keeping humans involved will improve the results of decision-making (making them safer or more accurate), and whether, and when, non-accuracy-related values—legitimacy, dignity, and so forth—are vindicated by the inclusion of humans in decision-making. Here, we take up a related but distinct question, which has eluded the scholarship thus far: does it matter if humans appear to be in the loop of decision-making, independent from whether they actually are? In other words, what is stake in the disjunction between whether humans in fact have ultimate authority over decision-making versus whether humans merely seem, from the outside, to have such authority?