Cognitive decline often surfaces in language years before diagnosis. It is frequently non-experts, such as those closest to the patient, who first sense a change and raise concern. As LLMs become integrated into daily communication and used over prolonged periods, it may even be an LLM that notices something is off. But what exactly do they notice--and should be noticing--when making that judgment? This paper investigates how dementia is perceived through language by non-experts. We presented transcribed picture descriptions to non-expert humans and LLMs, asking them to intuitively judge whether each text was produced by someone healthy or with dementia. We introduce an explainable method that uses LLMs to extract high-level, expert-guided features representing these picture descriptions, and use logistic regression to model human and LLM perceptions and compare with clinical diagnoses. Our analysis reveals that human perception of dementia is inconsistent and relies on a narrow, and sometimes misleading, set of cues. LLMs, by contrast, draw on a richer, more nuanced feature set that aligns more closely with clinical patterns. Still, both groups show a tendency toward false negatives, frequently overlooking dementia cases. Through our interpretable framework and the insights it provides, we hope to help non-experts better recognize the linguistic signs that matter.