This work examines the structural influence of low-credibility narratives and the comparative role of automated accounts (bots) versus human users on social media platforms. To more accurately quantify the structural influence of a narrative on social media, this study proposes two novel metrics: (1) Appeal, which measures the network-weighted popularity of a message; and (2) Scope, which measures an author's message popularity-weighted network penetration. Applying these metrics, this study analyzes 5.8 million messages from X that contain low-credibility narratives regarding COVID-19 vaccine across three distinct temporal stages: Pre-Vaccine, Vaccine Launch, and Post-Launch. The results demonstrate that across all timeframes, human-distributed low-credibility narratives achieved higher structural influence compared to those generated by automated accounts. Furthermore, statistical analysis reveals a significant conditional temporal effect: human-driven low-credibility narratives attained their highest Appeal and Scope during the focal Vaccine Launch week, whereas automated accounts maximized their Appeal and Scope during the highly uncertain Pre-Vaccine period. These findings highlight the distinct operational capacities of automated and organic accounts, illustrating how the Appeal and Scope of low-credibility narratives is moderated by the lifecycle stages of critical public events.