Incoherence in accountability relationships can hamper the quality of education. Such incoherence can be a particular challenge in resource-constrained, remote villages where teachers tend to have higher educational capital and social status than the parents and communities that they serve. We analyze quantitative and qualitative data from a randomized controlled trial of a social accountability mechanism (SAM) for schools in remote Indonesian villages. The intervention had three treatment arms, all of which included the SAM, which engaged village-level stakeholders in a consensus-building process that led to joint service agreements for supporting the learning process. Prior analyses have found that all three treatment arms significantly improved student learning, but the treatment arm combining the SAM with performance pay based on camera-monitored teacher attendance led to much larger gains than the SAM-only treatment or the treatment arm combining the SAM with teacher performance pay based on a community-evaluated scorecard. Drawing on a range of quantitative data sources across all treatment schools (process monitoring, survey, and service agreement indicators) and qualitative data from nine case study schools (interviews and focus group discussions), we show firstly that the student learning gains across all three treatment arms were accompanied by increases in the coherence of the accountability relationships between village-level stakeholders, and in the degree to which these relationships were oriented toward the purpose of cultivating learning. We further show that the treatment combining SAM with camera-monitored teacher performance pay led to greater improvements in the coherence of accountability relationships than the other treatment arms, because the cameras improved both the technical capacity and the social legitimacy of community members to hold teachers accountable. This coherence-focused, relational explanation for the relative effectiveness of the treatment arms has more explanatory power than alternative explanations that focus narrowly on information quality or incentive structure. Our analysis reinforces arguments for ensuring that accountability structures are coherent with the local context, including local social structures and power dynamics.