From the size and shape of the fruits, the name was an obvious choice, at least for English- and Spanish-speaking colonists.
Bala de cañón is indeed another moniker of Couroupita guianensis. But for native inhabitants of tropical South America, where European botanists first took note of it in the 18th century, more-familiar points of reference gave rise to common names such as mountain calabash, monkey's coconut, and stinking mamey.
The fruit is reportedly edible by humans, but that last name suggests why the tree is cultivated primarily as a curiosity. Both wild and domestic animals have been observed to eat the pulp once the ripe globes fall and split. Other animals, lying in wait for insects that seek out the showy flowers, find the fruits a handy perch, as you can see from the final two photos below.
Fairchild Tropical Botanic Garden
10901 Old Cutler Rd., Coral Gables, Florida
(From an autumn 2012 visit)