You've asked an excellent question!
Basically, there are two sources for shell stock for aquaculture. The wild and hatcheries. Quite obviously, hatchery rearing shell stock or gathering juveniles in the wild and raising them to adult sizes for grafting are cultural events. Natural pearls originate or form after the fact in either scenario. The question arises whether there was human intervention "by any means".
Even something simple as relaying is considered a means. In my operation, I am acutely aware of this dilemma. I work within both wild stocks and relayed grow-out areas and maintain their distinctions. To culture pearls, you need donors. If any are rejected for whatever reason, they are sent back to the reef, BUT within a segregated area so that if any pearls were to spontaneously or reactively create pearls, they cannot be deemed natural. Even if the major portion of mussels on that reef are natural. The same can be said about grafted pearls, after all they are returned to the reef too, but tagged as cultured.
Although the ocean has numerous ways of damaging shell stocks, whether by logs cast ashore, tumbling stones or parasitical infestations, those are natural events. That is why when I or others tread in my work sites, it's absolutely necessary to tread lightly and/or harvest with extreme caution, as not to disturb, crack or infect adjacent wild mussels.
This is why you rarely, if ever see farmers dealing in natural pearls, even knowing full well they occurred spontaneously. Keshi pearls are not natural, because grafted tissue did not adhere or indirectly adhered to the nucleus, yet became biomineralized all the same.
Natural pearls can only be classified as such, if they are harvested from wild specimens in otherwise previously undisturbed beds. Very often, after surveying a reef, I rarely (if ever) return there during the natural life cycle of the species.
If or whenever my cultured operations becomes viable, I will not claim any natural pearls occur there. Not necessarily because it's true, but because of the perception of it.