When dealing with a problematic user, it is beneficial to be able to see if they have behaved badly in general. Especially in the case of spammers, one of the greatest indicators that a post is promotional is if they are making similar posts across multiple sites, however, if other sites have removed the SPAM posts prior to reviewing their post, there is currently no easy way to tell if they are simply a new user who happens to have genuinely felt that a product was helpful to the question or if they are posting a self promoting link.
If diamond moderators were given the ability to see deleted posts on other sites, at least by users who have an account on a site they moderate, it would allow much better understanding of the intent of a user and aid determining if they are a problem user or not.