Does AI understand human values? While this remains an open philosophical question, we take a pragmatic stance by introducing VAPT, the Value-Alignment Perception Toolkit, for studying how LLMs reflect people's values and how people judge those reflections. 20 participants texted a human-like chatbot over a month, then completed a 2-hour interview with our toolkit evaluating AI's ability to extract (pull details regarding), embody (make decisions guided by), and explain (provide proof of) human values. 13 participants left our study convinced that AI can understand human values. Participants found the experience insightful for self-reflection and found themselves getting persuaded by the AI's reasoning. Thus, we warn about "weaponized empathy": a potentially dangerous design pattern that may arise in value-aligned, yet welfare-misaligned AI. VAPT offers concrete artifacts and design implications to evaluate and responsibly build value-aligned conversational agents with transparency, consent, and safeguards as AI grows more capable and human-like into the future.