It's not true. You can never see who downvoted you (a good thing, imo).
I heard, more and more such features get unlocked when you get more karma. Thanks for making it clear about down vote stuff.
The ability to downvote gets unlocked when you get enough karma. There are other abilities (e.g. creating a poll, flagging posts). I don't know whether there's a definitive list with thresholds anywhere (possibly in the Arc source code to HN).