Most of my response below was written in a response to someone posting a related article on Facebook.
The protest that sparked this protest was based on a federal judge opinion behind an incident where a woman and her friends held a dance vigil within the rotunda on Jefferson's birthday. You can read the text of the decision here: http://www.cadc.uscourts.gov/internet/opinions.nsf/748BE2DE8AF2A2A485257893004E07FC/$file/10-5078-1308285.pdf
The protest of this judge's opinion was filmed and in the video, rough arrests were made. Now, I do not condone the violence with which those arrests were made, but given how combative the protesters were when challenged, arrests were warranted.
Demonstrations are not allowed in all of 5 areas in all of Washington, DC, including inside the Jefferson Memorial as defined by the outer columns of the memorial. By holding a demonstration there, they were violating federal administrative law - http://cfr.vlex.com/vid/7-96-national-capital-region-19768726
Of particular note from the judge's opinion is the distinction that the inside of the Jefferson Memorial is defined as a non-public forum dedicated to solemn commemoration. Or, in other words, while not a physical graveyard site, this Memorial carries the same atmosphere as a graveyard site. That is one definition of memorial - an object or structure created in remembrance of someone who has died. A grave marker is a memorial. The Jefferson Memorial is a memorial.
Is it respectful, then, to dance on the graves of the dead?
That said, it is legal to dance at the memorial. It's in bad taste, but it's still legal. It is *not* legal to organize a public demonstration inside the memorial. Here's the exact language of the law from cfr.vlex.com site on what constitutes a demonstration -
"(g) Demonstrations and special events (1) Definitions. (i) The term demonstrations includes demonstrations, picketing, speechmaking, marching, holding vigils or religious services and all other like forms of conduct which involve the communication or expression of views or grievances, engaged in by one or more persons, the conduct of which has the effect, intent or propensity to draw a crowd or onlookers. This term does not include casual park use by visitors or tourists which does not have an intent or propensity to attract a crowd or onlookers."
They can dance near, and even on parts of the monument. Demonstrations are not allowed in the area that starts from the outermost surface of the outer columns and moves inward. From the three steps past those columns and outward, you can dance as much as you like. The area at the landing of those first three steps is at least 15' to 20' deep. Here's an overhead shot for reference - http://www.criticalpast.com/app_old/cpdata2/65675075811/big/65675075811_000023_3.jpg ... plenty of room for dancing, there.
I recognize that we have the right to assemble, but that comes with the responsibility to do so in an orderly fashion. If the original dance vigil and flash mob had organized just a few steps away, outside the rotunda, this would be a non-issue as long as there were less than 25 participants. And for more than 25 participants, they could have applied for a permit from the National Park Service, as long as they gave them a few weeks notice.
Just as we have laws against Westboro Baptist Church holding an organized demonstration right on the site of a military funeral (they have to be more than 300' away from the cemetery), we have a law that says people can't hold organized demonstrations at what is effectively a satellite grave site.
I think it's a fair balance between 1st Amendment rights and common decency. For what few places there are where demonstrations aren't allowed for reasons of safety or respect (again, there are only 5, three of which are also memorials to the dead), any other public space defined as such is fair game...as long as it follows the rules regarding acquiring a permit when applicable.