Starting with the assumption that all is based in random events yields no more than that when looking at evidence from nature. There are clues which could be interpreted as not random but that wouldn't fit the desired explanations, would it? Every time a gene is changed, there is the possibility that the change was not an accidental random event. However, it is also just as likely that only rarely does the Creator make small adjustments thus Science would be hard pressed to find the events other than by inference. Such an inference is the advent of spirit possessing beings ... when did our ancestors begin to bury their dead instead of leaving them for consumers? When did our ancestors begin helping others too old and unable to chew their food? When did our ancestors begin to paint upon their surroundings? Can Science prove these differences were gradually occurring instead of sudden behavior changes and thus possibly due to small Creator interventions?
Starting with the assumption that all is based in random events yields no more than that when looking at evidence from nature. There are clues which could be interpreted as not random but that wouldn't fit the desired explanations, would it? Every time a gene is changed, there is the possibility that the change was not an accidental random event. However, it is also just as likely that only rarely does the Creator make small adjustments thus Science would be hard pressed to find the events other than by inference. "Random" in scientific discussion means that the result cannot be exactly predicted. This may be due to insufficient knowledge about the conditions or it may be due to a weakness in the theory. The word "random" can be replaced by words indicating that the result is left to God without disturbing the theory.
In the case of evolution, the conditions surrounding specific changes are unknown and the theory says nothing about the cause. There are many possible causes (radiation, chemical effects, inaccurate replication, ...) all of which are under the control of the creator.
BTW, randomness in quantum theory is due to a "weakness" of the theory in that it only predicts the probability of an outcome. The theory further states that this weakness is insurmountable. The theory does not, and cannot, say that God doesn't make the ultimate decision.