The field of educational measurement places validity and fairness as central concepts of assessment quality. Prior research has proposed embedding fairness arguments within argument-based validity processes, particularly when fairness is conceived as comparability in assessment properties across groups. However, we argue that a more flexible approach to fairness arguments that occurs outside of and complementary to validity arguments is required to address many of the views on fairness that a set of assessment stakeholders may hold. Accordingly, we focus this manuscript on two contributions: (a) introducing the argument-based fairness approach to complement argument-based validity for both traditional and artificial intelligence (AI)-enhanced assessments and (b) applying it in an illustrative AI assessment of perceived hireability in automated video interviews used to prescreen job candidates. We conclude with recommendations for further advancing argument-based fairness approaches. [For the corresponding grantee submission, see ED620206.]