Do any of these services give you any insight into what variable drove the decision? I get that they can tell you the target variable (e.g. these people are likely to buy), but can they tell me that the age and gender fields had a higher correlation than income or education?
Most of them can. I have a doubt for Google Prediction, need to check... Also with BigML you get a decision tree model which allows to "explain" predictions with a list of decisions based on the values of the fields (see #3 on https://bigml.com/features).