Dan Riehl has posted about an incident in which high school kids spontaneously sang the national anthem at the Lincoln Memorial in Washington. A park cop came along and told them to shut up, that singing wasn't allowed at the Lincoln Memorial because it is a "content-neutral" site.
I'm probably in the minority here, but I don't think the cop was totally out of line. Some national monuments deserve a respectful silence. I wouldn't want people singing songs, even patriotic ones, in front of the Tomb of the Unknown Soldiers either, or anywhere at Arlington Cemetery. The songs would disturb the feeling of reverence and meditation.
Now for Ted Kennedy's grave, songs should be allowed, but only those appropriate and representative of the life and values of the Senator. Like "Chug-a-lug"or maybe "Dang Me" by Roger Miller.