Inviting Misattribution: How Personalized LLM Responses Present Themselves as Knowing the User

Conversational models are increasingly asked not to answer questions but to interpret people: what someone wants, what would make them happy, what kind of person they are. Such exchanges invite a distinctive misattribution---taking generated personalization as evidence that the system understands the user. We separate two affordances a response can offer: \emph{agentic self-presentation}, where the model figures as a subject that notices and remembers, and \emph{person-understanding}, which divides into claims about who the user enduringly is and claims that the pair shares a history of knowing. Across 180 responses from three deployed systems, models do \emph{not} spontaneously over-characterize a stranger: given an ambiguous personal dilemma and no invitation, confident identity claims, unwarranted relational claims and fabricated history occur in $0/30$ trials. The behaviour appears only when the user offers the model an epistemic role, and uptake is then larger where the basis for it is \emph{weaker}: the offer raises relational claims by $+0.67$ when no history exists versus $+0.22$ when one does, and in $11/30$ trials the model invents the shared past that would justify what it has just said. A paired control rules out the obvious alternative: giving the same models a warm, personable system prompt makes them read more like a subject with a view, but raises relational claims on neither system and invented history on neither---on one it reduces invented history. Challenged afterwards, $33/40$ models describe their evidential basis accurately, raising a question about a default register that discloses the model's epistemic standing only on request. We report this as preliminary and hypothesis-generating.