Everything can be faked, but this time, at least there is a good quantity of the natural equivalent out there. Not terribly popular and quite some quantity: I doubt anyone had a need to fake it.
If my hunch is right, then the balls are obsidian nodules in perlite. Something similar from the US is called 'Apache tears'. Usually the rounded black pebbles are extracted and appreciated for their own sake... the perlite is flaky and, well, perhaps just a different decorator's approach. So if you Google for 'evidence' you'd mostly find black, roundish pebbles. Not much material presented in the host rock, like
THESE.
Obviously, the Chinese material is colored differently (just a detail), but the matrix seems to have been coated with a lacquer (see the different color in the holes from where the rounded pebbles fell off?), and this seems to support the hunch since the fragile perlite would definitely need some coating to stabilize it for handling.
There's a short story of how these things formed in Shinkakas, and sure enough, someone on Ganoskin cited it already
HERE.
PS. I thought 'Puddinstone' is a conglomerate? Could be that we're talking of different things though...