We examine a previously undiscussed interaction between tense and predicates of personal taste (PPTs). While disagreements involving delicious or fun are generally considered faultless – they have no clear fact of the matter – we observe that, in joint oral narratives, this faultlessness varies with tense: if the narrative is told in the historical present, disagreements involving a PPT are not faultless. Drawing on narrative research in psychology and discourse analysis, we propose that this contrast reflects a pragmatic convention of the narrative genre that participants construct a consensus version of what happened from a unitary perspective. To link this pragmatics with the semantics, we adopt a bicontextual semantics, where the perspectival parameters for both PPTs and tense are located in a context of assessment (and not context of utterance). We show that when these contextual parameters are constrained by the unitary perspective of narratives, the present tense leads to nonfaultless disagreements, as its semantics tightly binds the temporal location of an event to the parameter relevant for appraisal. The past tense, by contrast, enables both faultless and nonfaultless disagreements. We derive this flexibility by revising the existing semantics for past tense, engendering a new perspective on crosslinguistic variation in tense usage.