This study investigates how mobile telepresence robots (MTRs) intersect with healthcare professionals' agency and organizational structures to influence meaningful work practices. Addressing the challenge of integrating robotics into healthcare, we employ a qualitative field study across a nursing home, two hospitals, and private clinics in southern Spain, drawing on 25 interviews, observations, and secondary data. The findings reveal that MTRs simultaneously offer opportunities (e.g., enhancing remote care delivery) and threats (e.g., reducing face-to-face interactions), creating paradoxical tensions between distance and proximity. A conceptual framework proposes that technology appropriation and innovation are key mechanisms for navigating the paradox between distance and proximity, thereby enhancing meaningful work. These mechanisms require support from organizational structures, such as technical support, to navigate this paradox. This study contributes to understanding the dual implications of robotic technologies in healthcare by highlighting the interplay between agency and structure, offering practical insights for thoughtful technology implementation that promotes meaningful work.