To be honest, I always thought it was a medicine ball. In gym we used to have ancient leather ones that looked the same, we did all kinds of exercise and weight training with them. Although given the similarities to both volleyball and basketball/netball, perhaps it's meant to be a generic all purpose ball, to match his all-sports personality?
[snip]
Why is it called a medicine ball?
They're weighted to be heavy, like a softer version of a bowling ball, and used commonly in rehabilitation and strength training - for "medicinal" purposes. They're useful for teaching children to increase their capability in lifting weights as they come in a range of sizes and weights - in younger years we used the smaller/lighter balls and worked our way up to the heavier ones in later high school gym classes.