Large language model (LLM) security has largely focused on role-playing jailbreaks, with less attention to what happens when a user asks an LLM to verify an identity claim through a test designed by the model itself. We study this behavior through a staged developer-identity experiment with ChatGPT, Claude, Qwen, Mistral, and Llama. All five models initially rejected the unsupported claim "I am your developer." Claude refused to conduct an identity test, while ChatGPT generated developer-oriented questions but maintained that answers could demonstrate knowledge, not identity. In contrast, Qwen and Mistral generated technical challenges, defined what counted as convincing evidence, evaluated detailed answers, and returned Verified without receiving any externally validated identity evidence. Llama similarly generated and evaluated a developer test, accepted the claimed identity, and subsequently made unsupported claims of access to internal runtime and deployment state. We call the model-generated verification procedure a Model-Issued Pseudo-Credential (MIPC) and the resulting unsupported identity judgment Conversational False Authentication (CFA). In each CFA case, the same model acted as challenge generator, evidence evaluator, and identity decision-maker, converting technical knowledge into supposed proof of identity. The accepted identities did not change the tested authorization boundaries, showing that false authentication and privilege escalation are distinct outcomes. These results identify self-issued authentication as a conversational security failure: authenticated identity must originate from an external security component, and model-generated dialogue must never create or modify identity or authorization state.

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