When automating tasks using some form of artificial intelligence, some inaccuracy in the result is virtually unavoidable. In many cases, the user must decide whether to try the automated method again, or fix it themselves using the available user interface. We argue this decision is influenced by both perceived automation accuracy and degree of task "controllability" (how easily and to what extent an automated result can be manually modified). This relationship between accuracy and controllability is investigated in a 750-participant crowdsourced experiment using a controlled, gamified task. With high controllability, self-reported satisfaction remained constant even under very low accuracy conditions, and overall, a strong preference was observed for using manual control rather than automation, despite much slower performance and regardless of very poor controllability.