Pharmaceutical companies developed COVID-19 vaccines in record time. However, it soon became apparent that global access to the vaccines was inequitable. Through a qualitative inquiry as the pandemic unfolded (to mid-2021), we provide an in-depth analysis of why companies engaged with the COVID-19 Vaccines Global Access Facility (COVAX), identifying the internal (to the company) and external factors that facilitated or impeded engagement. While all producers of the World Health Organization (WHO)-approved vaccines engaged with COVAX, our analysis highlights the differential levels of COVAX engagement and identifies contractual obligations, opportunities and company strategy, and reputational pressures as key explanatory factors. We discuss our empirical findings relative to the literature on political corporate social responsibility (PCSR). Accordingly, we question whether pharmaceutical companies lived up to their responsibilities as corporate citizens and conclude that they failed to fulfil the implied responsibility of combating inequitable vaccine distribution. We conclude with implications of our research for practice, in relation to the challenges of global access to COVID-19 vaccines and for access to medicines more generally.