So the white house is a park?

They tell you that a permit is required for commercial filming.
Backing up that everything relates to commerce.

In Canada all Parks Federal and Provincial are called lands of Canada.
Separating them from Crown land.

http://geogratis.gc.ca/api/en/nrcan-...f3d5e6ddb.html

This Canadian national map geographically illustrates the location of Canada Lands. Canada Lands include the Yukon, Northwest Territories and Nunavut, over 2600 Indian Reserves, Canada's National Parks and Historic Parks, and Canada's offshore area.