If the US (FBI) should investigate this killing? It is not cut and dry or you would not have numerous members of congress insisting on an investigation.
Numerous members of Congress can agree on investigating literally anything. Congress is full of whackjobs.
Besides, presented as such: American journalist got killed - maybe targeted! - by a foreign soldier, should the FBI investigate? Everyone will say "Hell yes!!!! Add to that that many believe that Israel is an occupying force committing genocide, and the answer becomes even stronger.
But if you zoom out and present it as: American ally soldier mistakenly killed a journalist in a cross fire in a war zone. An investigation was conducted with the involvement of US authorities. The US does not investigate allies and relies on their investigations. Should this country be singled out for an investigation?
The only thing cut and dry about this is that the announced independent investigation was a political announcement.