There's a trick there. They remove all administrative costs, all prevention costs, all money that are spent by all government except for one specific department, and then declare that's "real" spending. As if all the other money is not spent, towards the same goal. And, I suppose, they compare it to full spending in NYC (not sure since the second article is paywalled). But whatever happens in NYC, counting only net spending on shelters makes no sense - the money spent on all programs in that area, including of course their admin costs, should be counted. If admin costs or non-direct spending is too high and not important for solving the problems of the homeless, if should be changed, not just ignored. If only 22% of the budget reaches the homeless, then maybe we should advocate first not for raising taxes, but for figuring out why the other 78% do not.

Then there's another trick - the money which were strictly defined to help only current homeless (so if the program worked for somebody and she is no longer homeless, or is prevented from being homeless by the program spending, that money not counted) and then divided by the number of people who has been homeless at any point, including those that aren't homeless now. The yearly figure is divided by cumulative number, not by average at certain moment. That's like dividing number of seats in the class not by number of students in each class at the same time, but by number of students that will use that room over a year, and arriving to conclusion that school classes have 0.1 seat per pupil and we need 10x seats.