Stories of unproven, disproven, or misleading health-related claims, and their impact on individual and public health, are commonplace around the world. Disquiet about such claims is ubiquitous and growing within public, clinical, scientific, and policy discourse, with law commonly presented as having an important role to play in addressing concerns. Action, though, requires regulators to account for competing considerations, including fundamental freedoms, cultural diversity, and the potential for law to exacerbate inequalities. The latter is particularly significant when assessing the veracity of marginalised beliefs. In practice, legal decision-makers walk a fine line between everyday tolerance and occasional intervention. Yet, legal research pertinent to these issues is surprisingly limited. Here, we argue that new knowledge, methods, and collaborations are needed to better understand how regulatory interventions relevant to contested claims are constituted; how they operate in practice; and how they relate to different political and social processes - including acts of public resistance (like campaigns and protests). Only once we are collectively equipped with such critical knowledge of the current nature and possibilities of regulatory relations will it be possible to collectively design more imaginative and inclusive legal responses.