Now that was a tricky question. All my research into this indicates that self-reports of driver behaviour and accidents usually are very unreliable and biased in various ways. So, what can we actually use them for? Well, such data can tell us things about how the human mind works, and possibly also something about why drivers behave as they do in traffic.
For example, studies on forgetting of crashes indicate how poor our memories are. This is similar to memory studies in the lab, but in a real setting, and can therefore tell us things about how we remember important/aversive happenings in real life.
.But we could also possibly understand why drivers do not correct their own dangerous behaviour in traffic. The responses given in questionnaires, if compared to actual behaviour, may tell us something important about this. For example, if drivers selectively remember certain aspects of their driving, this may be what is important to them. This could be a way to educate drivers, showing them the discrepancy between their self-image and reality.
Now, this is all very much from the top of my head right now, but I must say that if we are to learn from self-reported driving behaviour and crashes, I think we need a new take on how to use this kind of data.
As for your specific question about predicting crashes from self-reported driving behaviour, I think there is very little we can learn there, apart from the need to be very cautious with this kind of data.
As for references on which I base these statements, they can be found on my Rg page.