I must confess that I have heard that story since I was a small boy. I live quite near Camp Butler. Camp Butler National Cemetary was created by order of President Lincoln in late 1862. I might be mistaken, but, I believe that it is the oldest Military Cenetary in our system of National Cemetaries.
As you may or may not know, there are more than 850 Confederate graves there since it was converted to a POW camp in late 1862 and many poor southern boys died that due to weather and illness brought on by conditions with in the camp. And the tops of the stones are pointed as you say.
I was not aware that the stones only date back to 1906, thank you for that info. I was told that the reason for the pointed stones was to keep the guards from sitting on them.
There are also many German and Italian and one Korean POW from WW II buried there.