Correct, this is the truth. Not only is it possible that she is opening herself up to a lawsuit by removing posts, and removing members and denying membership, but she just may have also opened herself and the city government up to the same lawsuit by being part of the council and representing the city, by selective membership of this private group. An elected official or any representative of the city, in any official capacity should not be allowed to deny the information this group is claiming they provide about the city, for the city, by the city, to anyone.
I can't believe that this has been allowed to continue for as long as it has. The new Parkinson administration has been so transparent and available unlike the previous Mayor. Like the original poster implied, it's just not a good look and it perpetuates rumors that hint at favoritism for a few connected people and business owners. A "conflict of interest" is putting it mildly.