Unless gamers are even more obnoxious than my mental image of us, isn't this fairly easily solvable by writing back "I'm sorry you can't afford the game, $NAME. Tell you what, I keep a few copies around for reviews by magazines and the like, and would be happy to give you one. Your CD key is... Thanks for your continued support of indie game companies." You can then go on to mention non-monetary ways to compensate you, like mentioning your generosity on the front page of Reddit, which apparently works quite well.
The "I don't want to ask for a handout" factor alone will probably keep people in line. If you're worried, you can give their requests individualized attention and weigh the pros and cons of their sob story, but that is almost certainly not an effective use of your time.
How many emails do you think he'll get after the kid does write a love-letter to digg about how awesome Jeff Vogel is?
How many from other Indian and Chinese kids, and how many from scammers and dirtbags?
The unfortunate effect of rewarding a request for a freebie online is that it attracts dirtbags who will drown out the voices of the people you actually want to help.
If you think the stigma against begging will keep people in line, let me congratulate you on your good fortune to date. You clearly have never seen a good thing ruined by dirtbags or met such a dirtbag and heard them crow about how they lied/scammed/cheated their way into a share of someone else's generosity with nary a thought to those crowded out.
I guess that kind of marketing approach is something Jeff should consider as an indy dev, but a possible benefit to him from exposure doesn't seem to have much to do with whether handing out free CD Keys to every email with a SOB story is practical or effective at actually helping the people he would like to help.
The "I don't want to ask for a handout" factor alone will probably keep people in line. If you're worried, you can give their requests individualized attention and weigh the pros and cons of their sob story, but that is almost certainly not an effective use of your time.