Previous studies evaluating the social equity of transit-based accessibility to healthcare have failed to consider travel time uncertainty by assuming that transit always operates exactly as scheduled. Their analyses, therefore, tended to ignore travellers’ efforts to avoid being late to their healthcare appointments. These conventional approaches might overestimate accessibility and lead to inaccurate evaluations of social equity. This study aims to investigate how overlooking travellers’ risk-management efforts under travel time uncertainty might result in flawed assessments of equity in transit-based accessibility to healthcare facilities. Specifically, we compare the traditional accessibility approach to the robust space–time accessibility (RSTA) method, which considers travellers’ risk-management strategies (e.g., leaving early, choosing routes based not only on travel time but also travel time variability) depending on whether they are risk-neutral or risk-averse under travel time uncertainty. The RSTA model provides a more conservative, realistic, and user-centred view of transit-based accessibility. To demonstrate this, we conducted an empirical study of Columbus, Ohio, USA, using real-time transit big data. Our results show that traditional measures of accessibility that do not consider the impact of travel time uncertainty cannot accurately capture the social and racial inequity in healthcare accessibility via transit. However, the RSTA method reveals significant inequity in transit-based healthcare accessibility among residents in terms of their socio-economic and demographic status. Moreover, the conventional accessibility method evaluates the new bus rapid transit (BRT) service as promoting the accessibility of disadvantaged people, which the robust accessibility method revealed is not true.