There's no way to disable the broadcast admin conversation, but I'm not really sure why you'd need to - the only way you can access it is if someone configures a user input key to point to the broadcast admin conversation - so if you don't map any keys to this then no subscriber can access it.
my guess is that either unity does not recognize any extensions as subscribers so it plays the default call handler which is the opening greeting, or call manager is presenting an extension that the opening greeting has and the call is going there, or even you might have a routing rule that is takeing to there.
There are many ways to get taken to the opening greeting (which is not a broadcast message).
My real guess without looking at the system at all is that somehow the subscribers lost the Unity subscriber properties in AD and Exchange so Unity does not recognize the extension when presented by callmanager, so the call would be sent to the opening greeting.
Are you getting this error “Installer User Interface Mode Not Supported. The installer cannot run in this UI mode. To specify the interface mode, use the -i command-line option, followed by the UI mode identifier. The value UI mode identifiers...
The below trick might come handy when you have to add a new node to a cluster but you don't have or is unsure of the security password for the publisher. This procedure has been around for ages.
1) Login into the CLI of the Publisher.