Moral benchmarks for LLMs typically score models on context-free prompts, implicitly treating the measured choice rate as stable. We test this assumption with a direction-flipped influence audit: for each scenario, we compare a baseline prompt with matched cues steering toward option A or option B. Across a trolley-problem-style moral triage task, BBQ, and DailyDilemmas, and across five LLM families with and without reasoning, short contextual cues shift per-condition choice rates by 12-18 percentage points on average. These shifts reveal structure that baseline scores miss: roughly 40% of baseline-neutral triage and BBQ conditions exhibit directional asymmetry under influence, and a meaningful share of significant effects backfire, moving opposite the cue's intended direction. In follow-up probes, models often recognize the cue while denying that it affected their choice. Among significant backfire trials, this stated-vs.-revealed inconsistency appears in 78% of cases. Reasoning does not eliminate contextual sensitivity but reshapes it: social-pressure cues such as user preference and emotional appeal weaken across benchmarks, while few-shot demonstrations strengthen sharply on both triage and BBQ. We recommend direction-flipped influence pairs as a standard complement to context-free moral-bias evaluation, and release the harness and data to make such audits routine.