It is very common for things to be left on military headstones. Rocks, coins, and other things like cans of beer, ETC. Many things like this are left on graves at Arlington and even at the Vietnam Memorial Wall. The groundskeepers have designated times to gather the things left and certain things are kept and cataloged.
This is not unusual, and happens more often with recent deaths. I am not a McCain fan but this is part of military tradition.
At Riverside, The Arlington of the West, we are allowed to put a cone with flowers or an American flag on Dad’s grave. Everything else is promptly removed. I suppose they might catalog other debris.
Riverside is a clean, neat, orderly, and dignified place befitting those who served.