This article addresses markers of plausibility and felicity in Eurosceptic narratives on social media that are not based on facts but on sociocultural and contextual appropriateness. Appropriateness is understood here as the contextual fit for specific audiences which includes a range of social and situational factors involved in judgements about the conventionality and propriety of statements. I investigate the construction of appropriateness on Twitter, taking a narrative on the National Health Service in the context of Brexit as an example. I show how Eurosceptic narratives on social media become “truthy” and “sticky”, and how conditions of appropriateness are constructed on Twitter. I bring together approaches from narratology and digital anthropology to show how social media posts in political debate follow distinct evaluation criteria.