As generative artificial intelligence (AI) settles into everyday practices of inquiry, an old epistemological question returns in a new guise: when does a proposition a user takes from an AI output become something the user knows, and when is it rational to trust it as such? This paper argues that the characteristic failures of AI-mediated inquiry are precisely those that the justified-true-belief (JTB) tradition and its post-Gettier anti-luck refinements were built to diagnose, and it advances three claims. First, AI outputs inherit neither the presumptive warrant of testimony nor the reliabilist warrant of deterministic tools: unaudited trust in a calculator rests on a type-level reliability record, and for general-purpose generative models there is no type-stable process to which such a record could attach -- a practical form of the generality problem. Second, use that stops at obtaining an output turns generative AI into a Gettier machine: the user's fluency-based seeming of justification is disconnected from the truth of what is believed, and, as a clock running ten times too fast illustrates, sheer speed of production multiplies coincidental hits, inflating the appearance of reliability without improving the standing of any single hit. Third, the remedy is a three-step structure of use -- acquisition, understanding, independent verification -- whose first two steps answer to the classical belief and justification conditions and whose third answers to the post-Gettier sensitivity condition. The result is a stakes-indexed criterion of rational trust, justified true output (JTO), with an everyday test: "Had this been false, would I have noticed?" The criterion is defended against objections from over-demandingness, the extended mind, model improvement, and redundancy.

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