It is. The US Park police are responsible for the park land. MPDC is responsible for the sidewalks on the perimeters of the park land as well as the streets of DC. Park Police have mounted officers, and they know how to make good use of their horses for crowd control.
I still have my doubts about any police agency in DC actually charging any of these punks with crimes (if they are stupid enough to try and damage a monument or to hurl stuff at the vets). In a large crowd like that, I think you are pretty much on your own.