Securing appropriate driver responses to conflicts is essential in automation that is not perfect (because the driver is needed as a fall-back for system limitations and failures). However, this is recognized as a major challenge in the human factors literature. Moreover, in-depth knowledge is lacking regarding mechanisms affecting the driver response process. The first aim of this study was to investigate how driver conflict response while using highly reliable (but not perfect) supervised automation differ for drivers that (a) crash or avoid a conflict object and (b) report high trust or low trust in automation to avoid the conflict object. The second aim was to understand the influence on the driver conflict response of two specific factors: a hands-on-wheel requirement (with vs. without), and the conflict object type (garbage bag vs. stationary vehicle). Seventy-six participants drove with highly reliable but supervised automation for 30 min on a test track. Thereafter they needed to avoid a static object that was revealed by a lead-vehicle cut-out. The driver conflict response was assessed through the response process: timepoints for driver surprise reaction, hands-on-wheel, driver steering, and driver braking. Crashers generally responded later in all actions of the response process compared to non-crashers. In fact, some crashers collided with the conflict object without even putting their hands on the wheel. Driver conflict response was independent of the hands-on-wheel requirement. High-trust drivers generally responded later than the low-trust drivers or not at all, and only high trust drivers crashed. The larger stationary vehicle triggered an earlier surprise reaction compared to the garbage bag, while hands-on-wheel and steering response were similar for the two conflict object types. To conclude, crashing is associated with a delay in all actions of the response process. In addition, driver conflict response does not change with a hands-on-wheel requirement but changes with trust-level and conflict object type. Simply holding the hands on the wheel is not sufficient to prevent collisions or elicit earlier responses. High trust in automation is associated with late response and crashing, whereas low trust is associated with appropriate driver response. A larger conflict object trigger earlier surprise reactions.