Healthcare-associated infections (HAIs) remain a serious public health problem. In previous work, two models of an intensive care unit (ICU) showed that differing population structures had markedly different rates of Staphylococcus aureus (MRSA) transmission. One explanation for this difference is the models having differing long-term equilbrium dynamics, resulting from different basic reproductive numbers, R0. We find in this system however that this is not the case, and that both models had the same value for R0. Instead, short-term, transient dynamics, characterizing a series of small, self-limiting outbreaks caused by pathogen reintroduction were responsible for the differences. These results show the importance of these short-term factors for disease systems where reintroduction events are frequent, even if they are below the epidemic threshold. Further, we examine how subtle changes in how a hospital is organized-or how a model assumes a hospital is organized-in terms of the admission of new patients may impact transmission rates. This has implications for both novel pathogens introduced into ICUs, such as Ebola, MERS or COVID-19, as well as existing healthcare-associated infections such as carbapenem-resistant Enterobacteriaceae.