Earlier quoted context omitted.
People should probably use operating systems written by people who care about backwards compatibility. Ideally ones that are developed in the open.
If I am understanding the problem correctly... Apple implemented app signing by default in 10.8. Users can either turn this off in System Preferences (removing the error), or the LibreOffice team can pay the $100 annual fee to get a properly signed app.
Most users, however, won't know this workaround and it shouldn't be necessary to lessen the security of OS X just to use (or update) LibreOffice.
I'm sure the Document Foundation could afford the necessary app-signing.