The Anaphor Agreement Effect (AAE) is the cross-linguistic inability for anaphors to co-vary with Φ-agreement (Rizzi 1990; Woolford 1999), with languages making use of a variety of strategies that conspire to circumvent this effect. In this short paper, I identify and confirm a prediction arising from two previous observations by Woolford (1999) concerning the scope of the AAE, based on new evidence from Inuktitut (Eastern Canadian Inuit). I propose that anaphors in Inuktitut are lexically specified as projecting additional syntactic structure, spelled out as oblique case morphology; because Φ-Agree in Inuktitut may only target ERG and ABS arguments, encountering an anaphor inevitably leads to failed Agree in the sense of Preminger (2011, 2014). I moreover argue that this exact AAE pattern is previously unattested, yet is predicted to arise given the range of existing strategies. Finally, this paper provides evidence against previous detransitivization-based approaches to reflexivity in Inuktitut (e.g. Bok-Bennema 1991).