I beg to differ. While constructing a model there are often unknown relationships and parameters between variables for which you have to make assumptions. Like, for example, you suspect that two variables are related, but instead of digging in deeper and deeper in order to exactly resolve the relation you assume an e.g. linear relation, you fit the parameters to some data and move on. As long as you clearly present your methodology, I don't think there is anything wrong with this. The next guy can look closer and walk the extra mile, figure out a more rigorous relationship between the variables and improve your model. This methodology is not only common, it's also necessary: often the relationships between variables is so complex that being more rigorous does not improve the model because you add physical parameters/constants that you know little of and cannot measure with enough accuracy (or at all), so you're better off fitting them anyway (inverse problem). As to the usefulness, scientists "tamper" with the models all the time: Kepler tampered with the model of Copernicus, and Newton tampered with the model of Kepler. "Tampering" Newton's law for improving the result accuracy led to general relativity.
Your comparison to the Turk is just wrong. That was a straight-out hoax. An algorithm "trained" to represent some data still has value in representing these data, no matter how simple/non-rigorous it is. If the model is good, then it might even have some value in predicting the behavior of the system (in our case, the supreme court) even under different conditions (the "future"). In the model there are certainly correlations that the maker figured out by examining some data. Thus, the model can only be as good as the data that it is based upon. There is nothing wrong with improving the model as more data become available. Stubbornly sticking to the initial (wrong) estimates would be like saying that we should have dumped Newton's law of gravitation at birth because we didn't have a good value for G, instead of measuring G with higher accuracy.