LLMs are increasingly used to explain personal sensing data, translating traces of activity and mood into natural-language accounts of why an anomalous day may have occurred. However, such explanations can sound coherent and personally meaningful even when the underlying evidence is sparse or missing. We introduce epistemic overreach (EO) as a measure for cases where a generated explanation implies more than the available sensing evidence can justify. To audit how often and in what forms EO occurs, we obtained anomalous-day scenarios from three longitudinal sensing datasets of college students: StudentLife, GLOBEM, and CollegeExperience. Across activity, sleep, and affect anomalies, we generated 14,922 explanations using three LLM families -- Llama, Qwen, and GPT -- under two prompting conditions: one minimally constrained prompt and another prompt explicitly instructing models to bound claims to the data. For each scenario, we varied the amount of behavioral evidence available to the model to examine whether more evidence reduces EO. We evaluated each explanation using a structured rubric, decomposing EO into the dimensions of unsupported causal attribution, unacknowledged data gaps, overconfident language, temporal inconsistency, and diagnostic inference. We find that LLMs routinely attribute anomalous days to causes without sufficient support from the data, and that this pattern replicates across datasets, anomaly types, and model families. Further, providing richer context does not reliably reduce EO; bounded prompting helps but does not eliminate it. These findings suggest that evidential grounding should be a first-order evaluation criterion for LLM-generated personal sensing explanations, alongside fluency and plausibility. We argue that personal sensing explanations require evidential discipline: systems must distinguish what is observed, what is inferred, and what remains unknown.