Recent devices have had black pixels still have some power going through them. My first AMOLED was the Galaxy Nexus and you could, in a dark room, see a very slight "lit up" black screen. It was still much better black than an LCD could do, but apparently it saves power by leaving pixels "on" all the time?
Either way, that leaves me as never owning a device with perfect blacks
Also, don't AMOLED screens use more power on whites than LCDs, making the overall usage even or even worse on the AMOLED end? Obviously this would change with someone who almost always has blacks on the screen, but my experience hasn't shown a noticeable battery improvement with AMOLEDs.