Large language models (LLMs) operate over information held in their context window, but it is unclear whether they use that information by referencing it literally or by relying on a more general semantic gist. We address this question by transferring the Deese-Roediger-McDermott (DRM) false-memory paradigm, a standard method for eliciting gist-based memory errors in humans, to four LLMs spanning two architectures and two parameter scales. We test recognition of studied words, unrelated words, and critical lures across context lengths from 1k to 32k tokens, and measure responses both as discrete judgments and as a continuous probability that captures effects below the threshold of an overt response. We find that a gist-consistent false-memory signal is present in every model, even where overt false recognitions are rare, but that its expression as overt false memory is model-specific. Where false memories occur, they tend to increase with context length, and they do so even though the studied words remain available verbatim in the context, indicating that recognition is driven by gist rather than verification against the literal input. The DRM paradigm thus offers a controlled, psychologically grounded probe of gist-driven errors in LLMs.