In theory, we could use https://fullfact.org/about/api/ -- request an API token, and hold an index of URLs that FullFact has records on. These could then be noted when accessing sites via Playback.
Also need to look at IA's work, e.g. http://blog.archive.org/2020/10/30/fact-checks-and-context-for-wayback-machine-pages/ and maybe ask them about how it's done.