Bird eating and arboreality are not correlative events in snakes. In other words, just because ball pythons have been proven to eat birds, bush babies and squirrels in the wild does not mean that they are arboreal.
FWIW, out of 8 of the bird species that they have been proven to feed on, 6 nest in trees.
And no, not all of the birds and arboreal mammals ingested by ball pythons were nestlings who fell to the ground. It has been studied in published papers that male ball pythons are often seen climbing trees in search of prey.
So to answer the OPs question - I think they can be safely considered semi-arboreal when it comes to feeding patterns. If you had asked the question what do BPs eat in the wild, most people have no idea that birds and arboreal mammals make up a considerable part of their diet. The common misconception is that they are dedicated ground-dwelling snakes that eat mainly rodents.
However, that does not mean that you need to provide them with an arboreal set up in order to maintain proper husbandry. It does mean that if you wish to provide otherwise and do so properly, your snake will be just as happy.
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