I'm not sure how you purchased/funded the game, if it was from the Kickstarter, it's likely there's a database with whatever email address you gave GHI so it'll be trivial to check the email address if GHI have it set up right. So if you used the same email address it's not hard for them to verify. I don't think Steam will provide such direct contact info for purchasers (they could probably check against your account name but not your email address), not sure about Desura. I gifted the game on Desura to someone so gave them the confirmation ID, and they also sent their Desura account name and my account name and e-mail address, so I guess Chris can verify somehow the giftee owns the game.
Yeah, Steam seem very generous with developers providing keys, Greenlight developers can generally provide as many as they want AFAIK for no cost if the game isn't purchased on Steam. (I think it's understandable, the sales they lose to elsewhere is worth them tying as many people as they can in to the Steam ecosystem. And many people who get and use the keys probably never would have purchased a key so it's not a lost sale. The only cost to Steam would be the miniscule extra bandwidth and support cost.)
GOG are not quite so generous (I've read it depends on the precise agreement, either way their POV is also understandable) but plenty of Kickstarter games have provided GOG keys. Based on Chris's comments, it sounds like GOG are at a minimum, letting them provide keys to all people who purchased the game before it came out on GOG. Which makes sense, if the game wasn't even on GOG they couldn't purchase it on GOG anyway, so it keeps everyone happy.
