Research on trust in AI is limited to several trustors (e.g., end-users) and trustees (especially AI systems), and empirical explorations remain in laboratory settings, overlooking factors that impact trust relations in the real world. Here, we broaden the scope of research by accounting for the supply chains that AI systems are part of. To this end, we present insights from an in-situ, empirical, study of LLM supply chains. We conducted interviews with 71 practitioners, and analyzed their (collaborative) practices using the lens of trust drawing from literature in organizational psychology. Our work reveals complex trust dynamics at the junctions of the chains, with interactions between diverse technical artifacts, individuals, or organizations. These junctions might constitute terrain for uncalibrated reliance when trustors lack supply chain knowledge or power dynamics are at play. Our findings bear implications for AI researchers and policymakers to promote AI governance that fosters calibrated trust.