This paper studies how frontline operators override algorithmic eligibility decisions in welfare systems. Using a field deployment of a decision-support system (SARAL) in India, we analyze 260 housing welfare (PMAY) cases in which all applicants were classified as ELIGIBLE_BY_RULE. Despite this, operators rejected or escalated 52% of cases. We show that overrides are systematically associated with unstructured signals in field notes, including material-affluence proxies, contextual spillovers, normative heuristics, and administrative constraints that are not encoded in the formal rule system. Because observational data conflates operator-specific judgment with contextual interpretation, the paper proposes a controlled experimental design using synthetic profiles and a dual-assessor structure to estimate the effect of these signals and distinguish between idiosyncratic bias and institutionally aligned decisions. The findings highlight a fundamental gap between algorithmic rule formalization and real-world administrative decision-making.