I believe that the DJ set up in an HOA common space grassy area next to the pool. This area did not require a residence keycard to access, but is still an owner common space, not a "public park."
-PJ
I live in an HOA governed community, and the HOA/community actually owns the roads and everything inside the main entrance. It's all private property... we pay for the roads, the street lights, etc.
I don't know what the arrangement is on this community we're discussing, but I have read that the outsiders/crashers were inside the clubhouse/pool area and even in the pool... and all of that is private property.