They can be is the answer
For the area we have marked, its simply free range, as is most of the park, but if we wanted one an area with a shelter, then we would need to fill out permits and such. If we had a few dozen people, that might not be such a bad idea, but as it sounds like we're gonna have a handful, it might be overkill.
From the FPDCC.com page:
Q: Do I need a permit to have a picnic in the FPDCC, and if so, how do I get one?
A: If your picnic is for a group of 25 or more persons a Picnic Permit must be obtained. You can download an application for Picnic Permits online. You'll find this application and more information about Picnic Permits in Recreation, under Picnics.
Picnics of less than 25 people must respect the reservations of those holding permits.