System prompt configuration can make the difference between near-total phishing blindness and near-perfect detection in LLM email agents. We present PhishNChips, a study of 11 models under 10 prompt strategies, showing that prompt-model interaction is a first-order security variable: a single model's phishing bypass rate ranges from under 1% to 97% depending on how it is configured, while the false-positive cost of the same prompt varies sharply across models. We then show that optimizing prompts around highly predictive signals can improve benchmark performance, reaching up to 93.7% recall at 3.8% false positive rate, but also creates a brittle attack surface. In particular, domain-matching strategies perform well when legitimate emails mostly have matched sender and URL domains, yet degrade sharply when attackers invert that signal by registering matching infrastructure. Response-trace analysis shows that 98% of successful bypasses reason in ways consistent with the inverted signal: the models are following the instruction, but the instruction's core assumption has become false. A counter-intuitive corollary follows: making prompts more specific can degrade already-capable models by replacing broader multi-signal reasoning with exploitable single-signal dependence. We characterize the resulting tension between detection, usability, and adversarial robustness as a navigable tradeoff, introduce Safetility, a deployability-aware metric that penalizes false positives, and argue that closing the adversarial gap likely requires tool augmentation with external ground truth.