I never saw it as a real 'model', just a way of clarifying definitions, and making statements such as "I believe that {anything not a matter of fact}" null. It provides a way to distinguish between "I don't believe in invisible dragons in my basement." and "I don't believe in {immoral action}". I suspect the original intention was to validate a philosopher who got fed up with someone who hid behind 'I don't believe in that' in a discussion, after which the philosopher responded with evidence that the subject under discussion was factual.

It's really not my area at all, so I don't really have any well-developed opinions on this. My comment wasn't meant to be an endorsement of the model, I was just pointing out a similarity with a view in the mainstream literature. From a pretty uninformed perspective, it does seem to me that the direction-to-fit thing doesn't really get at what's important about the distinct functional roles of belief and desire, so I'm inclined to agree with your assessment.