The downside of statistical models has always been understanding and explaining why they do whatever they do. Any statistical model will generate a result, either right or wrong, but it's impracticable to figure out how it came up with that result: the only knob you have is training data.

"Symbolic" techniques are the usual first choice because in order to get them to work reasonably well (i.e. beyond the 60%-80% threshold), you have to understand what they're doing.