Much of the research quantifying volume and spread of online misinformation measures the construct at the source level, identifying a set of specific unreliable domains that account for a relatively small share of news consumption. This source-level dichotomy obscures the potential for users to repurpose factually true information from reliable sources to advance misleading narratives. We demonstrate this potentially far more prevalent form of misinformation by identifying articles from reliable sources that are frequently co-shared with (shared by users who also shared) "fake" news on social media, and concurrently extracting narratives present in fake news content and claims fact-checked as false. Specifically in this study, we use Twitter/X data from May 2018 to November 2021 matched to a U.S. voter file. We find that narratives present in misinformation content are significantly more likely to occur in co-shared articles than in articles from the same reliable sources that are not co-shared, consistent with users using information from mainstream sources to enhance the credibility and reach of potentially misleading claims.