This paper presents an intensional account of anaphoric accessibility, providing a unified analysis of anaphora with antecedents under negation and non-veridical operators. These include cases with double negation, bathroom-disjunctions, and modal subordination, which have previously received disparate analyses. Building on analyses of modal subordination (Stone 1999; Brasoveanu 2006), the paper introduces a flat-update dynamic semantics, where expressions with the potential to introduce a discourse referent do so globally, regardless of their embedding context. Constraints on anaphora are derived based on discourse consistency and a pronominal existential inference interpreted relative to possible worlds in the local context. The analysis uses intensional representations of discourse referents, which store information about their embedding context, and its relationship to speaker commitments, explaining constraints imposed by negation and other non-veridical operators in terms of presuppositions about discourse referents.