Connected and autonomous vehicles (CAVs) have revolutionized traffic systems, introducing mixed-driving environments where human-driving and driverless vehicles can coexist on the same roadways. This dynamic interaction has resulted in complex social driving behaviors, emphasizing the need for social trust management to balance interactions in mixed-driving environments effectively. This work presents our vision of a trust management framework designed for mixed driving environments. By gaining from the black swan theory, we address critical blind spots and vulnerabilities in current trust models. We offer insights into how trust relationships can be optimized in the face of uncertainty. Our approach aims to support reliable social networks and facilitate harmonious collaboration between human-driving and driverless vehicles, which promotes the safety and efficiency of mixed-traffic ecosystems.