The increasing volume of publicly available data brought about by digitalization offers researchers opportunities to examine public sentiment on various national and global issues. However, concerns linked to the use of publicly available data in digital research are insufficiently addressed. To ensure its ethical and trustworthy conduct, it is crucial to assess the public's perception of digital research with publicly available data. We conducted 10 focus groups with 75 participants from the German-, French-, and Italian-speaking regions in Switzerland, reflecting nationwide perspectives on digital research with publicly available data. Through a thematic analysis, four major themes emerged: (1) expectations toward actors and digital research with publicly available data, such as alignment with research standards to promote result validity, using research findings for societal benefit, and ensuring transparency on data use through informed consent; (2) concerns about data reuse for purposes beyond the study's objectives, especially for financial gain, as well as concerns about method reliability, data quality, and privacy; (3) mitigative measures to minimize potential harm, such as through the involvement of external oversight committees; and (4) supportive measures encompassing communication strategies to raise awareness and inform the public about the use of their data for research purposes. Our findings suggest public support for digital research with publicly available data provided that specific expectations are met. Developing a framework for legitimate digital research with publicly available data is identified as a valuable next step, with a focus on broadening public awareness on digital research with publicly available data through nationwide communication campaigns and introducing relevant oversight measures to foster trust.