As much as I can tell, freshwater pearl may come in convincing copper tones. And there are very dark brown ones among the natural 'black pearls' - if that's chocolate, think super bitter 90% cocoa, milk free chocolate. I am not sure what species produced those, but there are a couple of pearl growers on this forum that should know precisely
In my opinion, the chances to find a whole strand of freshwater pearls of natural copper color are slim. And a strand of natural dark brown saltwater pearls is impossible: I have never heard of any such strands offered anywhere at any price. Now, I might have missed allot of news; there's an endless supply of pearls out there!
When the treatment for brown 'chocolate' Tahitian pearls was first disclosed a couple of years ago, there was a bit of confusion on the natural/treated status of these pearls and whether matching natural color existed ... you may find references to mysterious, million-dollar natural chocolate strands in older press articles
As the treatment became accepted now (i.e. you can still find the brown pearls in every price range, disclosure and all), rumors of natural chocolate color have faded.
My 2c.
PS: I am not taking into account here some freshwater pearls with icky, mustard-colored (to put it politely! ) proteinaceous stains. That's hardly 'pearl color'. Now, everything is a matter of personal taste, in the end. Those things sell somewhere, to some folks... apparently.