It is a US Park - which is considered Public Domain for Rallies and Assembly, unless otherwise posted. The only way you can not Assemble in any area, is if it is Private Property. National Parks/Monuments are NOT private property. What these kids did, was the same as me going out in front of my house on the PUBLIC road, and dancing around. The cops can't arrest me for doing that, period. You think the people who stand in front of the Statehouse downtown, ask for permission? Unless the crowd is going to number in the thousands, where you could interfere with services to others, you have all the right in the world to stand in front of a building and assemble.
If you don't like BP Gas, you could go stand on a sidewalk in front of a BP Gas Station and hold your sign up. As long as you are not stopping patrons from using the facility (blocking the entrance or pestering) there is nothing that BP Gas Station could do to you...it is your RIGHT to be able to do this. Just like it is your right to REFUSE searches, REFUSE to give a drivers license or state id to an officer (All you have to do is identify yourself, there is no law that states you have to give them an ID Card), etc.....
I am in shock, by how many people think what was done by the Park Police in this video was acceptable.