I'm not a lawyer, so what do I know, but I assume the answer depends on the state.
My guess is that they would have an uphill battle. Our system leans toward the release of information.
Not only that, they are receiving tens of millions of taxpayer dollars. IMO if a group is doing that, their records, and everything about them should be available to the public. They want to keep things private? Then operate on private funds. Don’t take public money.