When you encounter something that is surprising, you should actually be surprised. Surprise means that either your model of the world is wrong or you're getting lied to. I think Fake Explanations has a relevant parable.

A common tactic in 'unbelievable statistics' is that they attempt to substitute one number for another number in a comparison and hope nobody notices. To delve further into defending against the dark arts, they use this particular statement to gloss over the slight of hand they perform...

To be clear, not all households living below the poverty line receive $61,194 worth of assistance per year. After all, many above the poverty line also receive benefits from social welfare programs (e.g. pell grants).

When you read it, your mental radar should go off like a banshee. They're trying to get your mind to accept that it'll "be doing a little rounding" and turn off hard checks on the numbers. A useful 5-second level skill to counteract this is to ask yourself exactly how many people are receiving these "pell grants and stuff" that takes up a (seemingly) negligible proportion of people[*]. A quick googling says over 100 million, aka more than twice the number of Americans living in poverty.

This pushes our numbers to 150 million recipients rather than 17 million. That's an order of magnitude of difference and brings us to a roughly expected ~$6900 spent per recipient. It strikes me as a little high, but not really shocking. It turns out that my model was, in fact, basically correct and it was just the article doing creative things with words and statistics.

[*]Alternatively, you can try to calculate the money spent on "pell grants and stuff" which comes to ~$700 billion. Apparently the US gives out over 126 million scholarships each year. Who'd have thunk it?

Edit: That's not to say I agree or disagree with moving to direct cash payments. I just felt a need to point out how the article was being such a tricksy little hobbitses.