Do we have to allow for the possibility? Sure. Do we have a felt need to bankroll it or teach it in school? Not obviously. Natural causes has turned out the be a satisfactory explanation for things we didn't previously know every time the question has been put to the test so far. Let's not be making stupid bets out of a sense of fairness.
I'm not suggesting that non-random causes are necessarily supernatural.
Isn't it possible for natural causes to also be non-random?