While Responsible AI audits are widely accepted as critical aspects of AI governance, they are most often conducted in a context of mutual trust, responsiveness, and cooperation. However, companies and organizations may lie, hide information, or neglect some aspect of the audit to make their AI system appear safer, more ethical, or more sustainable than it actually is, as illustrated by historical scandals in more established industries, such as the "Dieselgate". Indeed, if proper care is not taken to ensure the trustworthiness of Responsible AI audits in the face of dishonesty and negligence, these audits may be misused for ethics-washing instead of ensuring accountability and preventing harm. The goal of this tutorial is to foster a cross-disciplinary dialogue around a central question: what are the possibilities of cheating Responsible AI audits and how can they be reconciled? We address this by examining audits at the AI component (e.g., a model) and system level and bridging perspectives from multiplicity, cryptography, system safety, and measurement theory.