By doing this, you are making them legally legitimate to convey imprudent information.
No, the simple solution is to enforce public authorities not to use Facebook (or similar platform) as their main communication channel.
You know the saying "it’s easy to make a Twitter clone, it’s not easy to become Twitter". Well government don’t need to become Twitter, so what is stopping them to provide a "public" Twitter clone just for those communications ?
Seems like a simple solution.