Body hair grows because the follicles are genetically predisposed to grow. Now, a lot of males without much body hair in their late teens or early 20s can often prohibit much new growth while on anti-androgens. This isn't always successful, though, meaning we don't know how much androgens like DHT matter in new body hair growth.
Most people report that beard density continues to increase while on finasteride, though, and there are a couple of studies that show facial hair EXCLUSIVELY reacts to higher amounts of testosterone. Neither of the two studies I've seen on this were conclusive, but believed it was at least a causal factor.