Dammit, where's Eliezer Yudkowsky when you need him. I'm pretty sure he'll have an interesting take on this.
MBlume posted the article to LW here: http://lesswrong.com/lw/1b9/do_the_unlucky_systematically_un...
If you want me to say something stunningly intelligent about it, um... ah... okay, how about this:
Since we know at the start of the problem that luck in the supernatural sense doesn't really exist, we would expect people experiencing systematic exogenous runs of genuine good or bad luck to be rare in the population. But people who claim to be lucky or unlucky are much more common than that.
The next question you'd have to address is whether the people who claim to be "lucky" or "unlucky" actually seem to be experiencing more-than-chance proportions of good or bad life events, of a sort we would otherwise think of as exogenous (like falling down stairs) or partially randomness-based (like meeting a new girlfriend in a crowd). There would be a large problem of biased reporting at this point.
If so, then because we know luck doesn't really exist, we should indeed look for hidden internal characteristics to explain these runs of good or bad luck. As the saying goes, "YOU are the only common denominator in all your failed relationships."
Trying to train people to be lucky was an interesting attempt at experimental manipulation, but it's hard to untangle from the "biased reporting" hypothesis - you may just be making people think they're lucky. Still a good thing to test, though. (Possible stronger test: Train people to be "lucky in love" (that's what you tell them you're doing) and see if they become luckier in other areas too.)