Freshwater pearls from China ARE cultured, but not bead nucleated. Cultured is defined as any pearl formed which is the result of human intervention. Chinese FWP's are tissue nucleated.
You can get them anywhere. Nearly every online pearl dealer carries them, and most jewelry stores carry them, though quality and price will vary greatly between sources.
Nearly all freshwater pearls discussed on this forum are such pearls: cultured but w/o nucleus. Only a couple of threads discuss nucleated freshwater pearls - still something very unusual and very recognizable by shape. Take a look.
Natural pearls - not farmed, produced without human intervention have their own section on the forum ('Natural Pearls') that does contain a word or two about natural freshwater pearls, not Chinese but Scottish. Haven't heard anyone talking about any natural pearls coming from China, freshwater or otherwise. Not here, not elsewhere. Different matter this altogether.
It is somewhat confusing that 'natural' is used to describe either cultured pearls (as opposed to fakes that have never been close to a mollusk at all) or non-cultured (proper meaning) and more rarely cultured non-nucleated, as you say. Before this thread, I've only heard this third usage once or twice. The first seems common.
It is funny, but the same question of calling cultured freshwater pearls "natural" happens in India too. We just had that question on another thread. It really means, "no bead nucleus" in India, because the pearls they favor are imported Chinese cultured freshwater pearls.