I am going to guess that there is no headstone because she wants one that says something ridiculous on it and Casey's father wants to put down a normal headstone and she is fighting him on it.
Headstone's are too narrow for her to stand on.
You could well be correct. As I neglected to mention and another poster suggested to me, the military would purchase a stone for her son. Perhaps she was laying on it and it was not visible. But, all these shenannigans are for her self aggrandizement, not her son.