If an article, theorem, etc. is unpublished, presumably the work is only available to people who track down the author and get a draft copy. Today we have arXiv and can find many preprints on the Internet, but people have been citing unpublished works longer than arXiv has been around. It seems like an unscrupulous author could claim anything he wants, cite an unpublished work that doesn't support his claim (or even one that doesn't exist), and get away with it unless the bad claim is caught in the review process.
I suppose the reviewers could ask for a copy of the cited work, but I recently saw a citation that was just "private communication 1981" for a paper published in 1985, and that could easily have been a phone call where no record could be provided to a reviewer.
I've never published anything myself, so maybe I'm unaware of a part of the review process that is meant to catch this, but what prevents authors from making bad citations of unpublished works?