Introduction: The Mediterranean diet (MD) has been linked to better cognition, but evidence in older adults at high dementia risk is limited. Moreover, the traditional Mediterranean Diet Adherence Screener (MEDAS) counts daily wine consumption as a beneficial component, which may distort genuine diet–cognition relationships. Objective: Evaluate whether MD adherence, as measured with the original MEDAS (MEDAS-O) versus a version that reverses the wine item (MEDAS-R), is associated with cognitive function in Portuguese adults aged 55–85 years at increased dementia risk. Methodology: The sample comprised 75 participants from the NUTRIMIND randomised controlled trial (mean age 70.5 ± 7.0 years). MD adherence was evaluated using the original version of MEDAS (MEDAS-O) and an adapted version with a reverse score in the wine question (MEDAS-R). Cognitive function was assessed via the Montreal Cognitive Assessment (MoCA), Addenbrooke’s Cognitive Examination Revised (ACE-R) and Mini-Mental State Examination (MMSE). Statistical analysis was performed using Analysis of Covariance (ANCOVA) models adjusted for age, sex, BMI, education, and physical activity. Results: MEDAS-R was positively associated with better MMSE performance (p = 0.043) and showed a borderline association with the MoCA (p = 0.051), but not with the ACE-R score (p = 0.356). No association was found between MEDAS-O and cognitive function. Better cognitive scores were more frequently observed among participants with higher education (p < 0.001). Conclusions: Reversing the wine item changes how MEDAS relates to cognitive function. These findings support re-evaluating how wine is scored in MD adherence measures.