Have not read the article in depth yet, but I am very familiar with the Troyanskaya lab. They are good and their articles are always worth a read.

They are using a geodesic finite mixture model, which I am not familiar with, but seems to be an extension of mixture models to non Euclidean metric?

Pleiotropy can be tricky though, as traits / diagnoses / observations can have causal relationships amongst themselves. For example, a variant that impacts obesity may be statistically associated with heart attacks; but the relationship between the variant and heart attacks is not directly causal in the sense of something like a variant that alters function of an ion channel expressed in cardiac smooth muscle.