Looking at some of the chemistry behind grape juice it seems that there are traces ( varying according to variety and origin) of copper and zinc in most types.
Copper sulfate solutions are used for darkening zinc alloys so I'd guess that the trace amounts of copper in juice coupled with the various acids in the juice probably contribute to the darkening effect. I don't know the particular chem involved but a guess a combination of oxidation and some copper ion deposition.
Better that than the commercial nasty solutions..