@dschobel - you are right that it is difficult to learn complicated domain models in domains like this with a lot of subtle logic. To deal with this we use a blend of analytical and inductive learning. There is a nice discussion of combining analytical and inductive learning in "Machine Learning" - Mitchell, ch. 11 & 12.
As to the specifics of whether we use SVMs, Bayesean Networks, Decision Trees, and so on - we don't feel that it would be beneficial to get into detail.
This is not just to keep everything top-secret, but also because all of this is an area of active research and we may completely change the approach at any moment. Most of what gives us in an edge is 1) the ability to deal with the data (preprocessing, joining, etc.) 2) the infrastructure to do fast, distributed learning, and 3) the domain expertise to add richness of logic to the individual classifiers we use. The exact techniques by which we weave everything together are open to constant tweaking.
Another important point outside of the specific learning algorithms is that we use rigorous approaches like 100-fold cross-validation and such. But I like to think of it like Popper - so I call it invalidation rather than validation. :-)
IMO, the process of bringing scientific rigor to a problem is also more important than the hypothesis under test. A lot of the best stuff comes from a rigorous application of scientific method that yields unexpected results that lead you to a an alternative hypothesis.
That would be my first instinct if I had to solve this problem.