Well, Throbert, i will try to explain further: when ученик in the sense of 'disciple' is used in Russian it means than some Person(s) is (are) the disciple(s)/follower(s) of another Person (now, this particular usage is rare, forученик is mostly used in the other sense in school environment). So Аристотель - ученик Платона is correct (person-person), while Аристотель - ученик греческой философии (Aristotle is the follower of the Greek philosophy) is awkward in Russian. One of the correct variants could be Аристотель - последователь греческой философии (последователь - follower).

Coming back to 'Она была ученицей французской кухни' - they wouldn't say that in Russian. In case of Julia Child wikipedia in Russian says: Джулия Чайлд — американский шеф-повар французской кухни. Here Шеф-повар in Russian means she was a professional, skilled in the French cuisine field, master. Another variant that i could guess would be: "специалист по французской кухне" (French cuisine specialist).

ученик французской кухни - also sounds strange in Russian. If you just like cooking French food or you like French cuisine recipes you could be called: "любитель французской кухни" or "поклонник французской кухни" (admirer) (don't necessarily mean you use French cuisine recipes, it could be you just like eating French food, but also you like French recipes). I think most neutral would be: "Я люблю готовить блюда французской кухни" (I love cooking French cuisine meals), so here we are very far from the word "ученик".