I don't know for sure how they make medicine balls, but I would guess they would sew the top half first, then flip it over to work on the bottom, when half of the bottom panels are complete they could pull out some wedges and rotate the leather, then continue in this manner until complete.
I figured that most round pinatas were made by using a balloon for support. We'll have to agree to disagree on this one, but if you find any sources on wood pinata forms I'd be happy to take a look at them.
Someone had told me that 8" was too small for a medicine ball but I found one that size on this page: