Two commonly employed strategies to combat the rise of misinformation on social media are (i) fact-checking by professional organisations and (ii) community moderation by platform users. Policy changes by Twitter/X and, more recently, Meta, signal a shift away from partnerships with fact-checking organisations and towards an increased reliance on crowdsourced community notes. However, the extent and nature of dependencies between fact-checking and helpful community notes remain unclear. To address these questions, we use language models to annotate a large corpus of Twitter/X community notes with attributes such as topic, cited sources, and whether they refute claims tied to broader misinformation narratives. Our analysis reveals that community notes cite fact-checking sources up to five times more than previously reported. Fact-checking is especially crucial for notes on posts linked to broader narratives, which are twice as likely to reference fact-checking sources compared to other sources. Our results show that successful community moderation relies on professional fact-checking and highlight how citizen and professional fact-checking are deeply intertwined.