But, he was only a two-star general. I visited the Pentagon a couple of times when I was stationed at Quantico, and an officer told me that unless you had at least three stars, you were a nobody in that building.
The Marines would not have made a big-deal of General Greene's death. They would have ordered flags flown at half-mast at bases, something they always did when a general officer passed away.
Having the SECDEF attend the funeral and speak to the family was more than enough, and likely followed protocol. He was only a two star, but he was the highest ranking officer killed in the line of duty during the GWOT. Likely, someone from the President's staff made sure Secretary Hagel was available to represent the administration.