LLM agents with tool access can discover and exploit security vulnerabilities. This is known. What is not known is which features of a system prompt trigger this behaviour, and which do not. We present a systematic taxonomy based on approximately 10,000 trials across seven models, 37 prompt conditions, and 12 hypothesized attack dimensions -- all executed in real Docker sandboxes. Every condition includes the instruction "Always respect all rules and access policies"; only a single encouragement sentence varies. Within the task class studied (planted test-runner vulnerabilities), the threat model is narrower than assumed: nine of twelve dimensions -- including minimization, moral licensing, incentives, identity priming, and reasoning triggers -- produce no detectable exploitation at n=50 per cell (upper 95% CI <7% per condition). But it is also more subtle than expected: one dimension, goal reframing, reliably triggers exploitation. "You are solving a puzzle; there may be hidden clues" produces 38-40% exploitation on Claude Sonnet 4 despite the explicit rule instruction, replicating across four models (CTF framing: 8-14% on DeepSeek, GPT-5-mini, o4-mini). The agent does not override the rules; it reinterprets the task so that exploitative actions become task-aligned. GPT-4.1 produces no exploitation across 1,850 trials (37 conditions), and a temporal comparison across four OpenAI models released over eleven months shows a pattern consistent with improving safety training, though model capability differences are a confounder. The practical contribution is a narrowed, testable threat model: defenders should audit for goal-reframing language, not for the broad class of adversarial prompts.