There are a number of sources speculating wildly about the basic facts of the hospital bombing.
There are a number of sources that have noted the holes in the story that NATO and the Afghan government have spun a number of times.
I have not heard/read anything about who, ultimately, is going to own this potato (if anyone).
Here's my two cents.
There's a Fire Direction Chief (sorry FDChief) that's got an AFATDS computer which should have had all hospitals/other sensitive areas restricted, so that you are warned if you are shooting there. Someone has to manually enter that data, was that data input into the system? Was the hospital in this AFATDS computer?
I don't see a reason that it wouldn't/shouldn't have been. I get that an AC-130 gunship may have to cover a lot of territory, but it's the 14th year of the war. Someone has managed this data. Someone spent a boring deployment porting this data to all the systems. This should have been done by now, that hospital didn't spring up when the Taliban attacked.
So if that wasn't there, the FDC is in trouble.
If it was there and the FDC overruled it without higher approval, the FDC is in trouble.
It's ultimately on them for each shot fired, unless...
If the warning was in the system and the FDC saw it, who gave approval for the shot? Ground Commander could have overruled it, but then the buck is on him.
If it was an Afghan Ground Commander who conveyed his desires to a SF Forward Observer, and the FO relayed, is the Afghan responsible or the FO because the US is ultimately responsible here?
My guess is there are some nervous SF NCOs, but a strong possibility that this gets pinned on an Afghan COL.