The article makes the program sound reasonably humanitarian, while the initial description made it sound more like "dump the problem elsewhere". With the examples of homeless people who had relatives in France or Puerto Rico they could live with, but they just couldn't afford to get there, buying them plane tickets seems like an actual solution to the problem that's good for both the people in question and NYC. And it sounds like it's only done on request, not some kind of involuntary exile (compare: http://money.msn.com/now/post--columbia-sc-to-exile-its-home...).
I have no idea if the article is cherry-picking unrepresentative positive examples, though. To determine if it's solving or just shifting the problem, it'd be interesting if there were any statistics on what % of people NYC bought one-way tickets for were homeless again N months or years afterwards, vs. in a more stable situation. Admittedly it's probably quite difficult to collect reliable data on that.
More because it is a known fact that a large proportion of the homless in NYC are not actually even from NY and I don't think we should be paying to take care of people who are not actually from the area. This to me should be a federal issue, why should major metropolitan areas have to pay for all the joe smoes who move to the city for no other reason than mooching off the "better" benefits that cities provide over small towns.
And stop ducking the question, genius. Are you really trying to tell us that the solution to your homelessness problem is to bus people who you magically somehow don't think are from your area clear across the country to a place they almost certainly aren't from?