The religious groups do a better job than secular organizations simply because we have to be motivated by something other than a paycheck and, most importantly, we can discriminate like mad. We can pick and choose and leave the rest to the secular agencies to deal with. Gives us a killer track record and makes them look bad. Religious organizations that are willing to get in bed with the gummint have to be a bit suspect. As the essay says, religions by nature are particular and parochial and we follow Godde particularly, if not very successfully.
People are pretty complicated.
Accountability is about measurable success, about budget, which is about quantifying and therefore defining. The human condition doesn't lend itself to being boxed in thus. Human relationships also are neither definable nor quantifiable. Quantifying the relief of human suffering is mixing apples and oranges. It has no significance except to make folks sit up, take note, think a bit.