Official word from the Tribe Adventure Program, May 2nd:

"The campsites used for TAP programming are not labeled in an effort to discourage others from camping. We operate 6 campsites throughout Matoaka Woods and hang appropriate signage based on our permits with the police and fire departments. If you would like to mention anything about camping in Matoaka Woods, I would just make a note to say that camping is not allowed in Matoaka Woods unless on a W&M sponsored program that has been given approval and appropriate permits by the Williamsburg police/fire departments."

If I find campsites around the College Woods, I'll add them to OSM, but make it clear that they are not open for public camping.