Their theory is "the AZ vaccine causes clotting problems in people who (a) have some particular relatively common gene, and (b) have previously been exposed to a pathogen that is similar from their immune system's point of view to the adeno-virus that was used a vector". Point b means that the pathogen is something these people have been exposed to in the past: the only trace is the immune response that got reactivated, so identifying which particular pathogen it was is not easy.