It is not a recommendation problem, this is classical classification, nothing more. Neural Networks are just one of dozens od possible approaches,but once again - it is not collaborative filtering, it is exactly how classification is defined. In collaborative filtering you do not know the correct answer (labels/output) - you simply try to find some common pattern among other. In case of disease detection/forecast you know exactly what should be the output.
Recommender systems could be used here if you have very broad spectrum of possible, correlated diseases, and very small amount of people with it (so it is not possible to actually build training sets for the disseas). Then such "recommendation" which looks for a potential health problem would have sense.In case of labeled, binary output data it is just a classification. Even though, you would probably end up with model: "if you have obessity, then you will probably get a heart attack" etc. So finding correlation between similar diagnoses.