I'm not saying this makes it right in this case (it doesn't), but particularly when the school is not in session, it can be considered trespassing like any other place. It's public in the sense that it's offered to the public, it's still private property. You go snooping around a school after hours and I guarantee you're likely to get a trespassing charge if not worse.
This however, is totally different because I believe it was the chairman saying it, and they're convening after a caucus at the location, but make no mistake, it's still private property, just the same as if you wanted to go camping there or anything... It's not public in that sense, unless you're invited.