In the case of canned fish, the bones are usually so softened that you can simply eat them or stir them into whatever you're making with the fish and barely notice them. Eating the whole bones must provide even more full of the goodies from bones than whatever leaches out in the canning liquid.
A previous response noted Wild Planet, which doesn't even add water to most of their tuna. This is a brand I'm really starting to prefer. The fact that the tuna is cooked in the can during the process that preserves it, rather than being pre-cooked, then cooked again during preservation, really does seem to result in much better flavor and texture. Open one of these cans, and you find barely any liquid--and you don't even need to drain it.
But the tuna doesn't have bones, so I doubt the little liquid there is has much to offer, and Wild Planet seems not to make any claims about BPA-free cans--except for the sardines, whose BPA-free status Wild Planet is careful to mention on their website. AND, sardines do have bones that you can/should eat.
So once again, the diminutive but mighty canned sardine seems to rule.
UPDATE: Thanks to a comment below, I re-checked the website and found that Wild Planet indeed uses BPA-free cans. Sorry about that!