When a multi-module LLM agent fails, the module most responsible for the failure is not necessarily the best place to intervene. We demonstrate this Diagnostic Paradox empirically: causal analysis consistently identifies the routing module -- which selects which tool to call next -- as the primary bottleneck across three independent agent families. Yet injecting prompt-level correction examples into this module consistently degrades performance, sometimes severely. Patching an upstream query-rewriting module instead reliably improves outcomes. The effect holds with statistical significance on two agent families and directional consistency on a third; alternative repair strategies at the routing module (instruction rewriting, model upgrade) are neutral, confirming that the harm is specific to correction-injection patching. We explain this asymmetry through the Linguistic Contract hypothesis: each downstream module implicitly adapts to its upstream's characteristic error distribution, so correcting the bottleneck breaks this implicit alignment in a way that upstream corrections do not. We operationalize this via a per-agent co-adaptation measure, derived from diagnosis alone, and show it is consistently associated with patching harm across agent families: higher co-adaptation co-occurs with harm, lower with safety. This trend holds across all three agent families, providing preliminary support for the hypothesis beyond a single-agent observation.