In recent years, algorithms have been incorporated into fact-checking pipelines. They are used not only to flag previously fact-checked misinformation, but also to provide suggestions about which trending claims should be prioritized for fact-checking -a paradigm called 'check-worthiness.' While several studies have examined the accuracy of these algorithms, none have investigated how the benefits from these algorithms (via reduction in exposure to misinformation) are distributed amongst various online communities. In this paper, we investigate how diverse representation across multiple stages of the AI development pipeline affects the distribution of benefits from AI-assisted factchecking for different online communities. We simulate information propagation through the network using our novel Topic-Aware, Community-Impacted Twitter (TACIT) simulator on a large Twitter followers network, tuned to produce realistic cascades of true and false information across multiple topics. Finally, using simulated data as a test bed, we implement numerous algorithmic fact-checking interventions that explicitly account for notions of diversity. We find that both representative and egalitarian methods for sampling and labeling check-worthiness model training data can lead to network-wide benefit concentrated in majority communities, while incorporating diversity into how fact-checkers use algorithmic recommendations can actively reduce inequalities in benefits between majority and minority communities. These findings contribute to an important conversation around the responsible implementation of AI-assisted fact-checking by social media platforms and fact-checking organizations.