The field of educational measurement places validity and fairness as central concepts of assessment quality (AERA, APA, NCME, 2014). Prior research has proposed embedding fairness arguments within argument-based validity processes, particularly when fairness is conceived as comparability in assessment properties across groups (Chapelle, 2021; Xi, 2010). 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 pre-screen job candidates. We conclude with recommendations for further advancing argument-based fairness approaches. [This is the online first version of a paper that will be published in "Journal of Educational Measurement."]