Yes, it happened in nature, but as a, "one off" event and not, for instance, discovering say that blasting a high speed proton into a certain particle gave 5 up-quark gluons and not the predicted 3 up-quarks and 2 down-quarks. The events of the second case are repeatable and testable, whereas sudden healings are one-off events and not available for study.
Nobody claimed that God was detected. Some here said that we believe by faith that the unexplained healing was done miraculously by God in an answer to prayers.
God can do whatever he likes and he chooses be hidden in that way. There are reasonable explanations for the hiddeness of God, but they are neither here nor there for the purposes of this discussion. The above comment shows that you seem to have idea that, basically, because God doesn't appear on TV claiming His existence (or anything like that) then He doesn't exist. However, there is no a priori definition of God, and IMO no Christian theology either, that rules out that God created a universe that unfolds gradually over time without any special workings (which wouldn't be able to be detected anyway). His recorded redemptive acts are believed in by faith, as are any other miracles that He decided to do, as for instance a miraculous healing.