Amazon has a list of all the books in your library. It is not inconceivable that Amazon could provide a list of what books its users are currently reading/have

Amazon has a list of all the books in your library. It is not inconceivable that Amazon could provide a list of what books its users are currently reading/have in their library (including books they are lending) and providing such a list to the publishers/guild. Is that proof enough? Who knows. Is it easily faked? Yes. But that is always going to be the case with anything digital. You either choose to believe them or you don't.