The story is long, and has plenty of local color--from New York Chinatown--but it boils down to two points:
1) Asians buy produce daily, or at least more often than other Americans, so Chinatown vendors can buy riper produce. Regular supermarket chains pay more for unripe produce because it has a longer shelf life. Asian groceries have customers who will be using the produce sooner, so they can buy the cheaper produce which is much closer to being overripe.
2) Asians cook more, so they buy more produce. This means the Asian grocers also move a greater volume of produce, enabling them to buy in bulk, and thus pay less.
The take-away from this is that if you want cheap, ripe produce, get it from the Asian vendors. But it'll go bad more quickly.
(Up here in Boston, Haymarket also sells a lot of produce which is just this side of going bad, and it is also quite cheap, probably for similar reasons.)