Forgive my obtuseness..
Please explain what I am missing in your analogy.. (and please forgive my cut and paste)
An objective explanation of what a theocracy is or in what sense that term is used has to deal with two very different approaches.
* For believers in a religion whose institutions have been more or less equated with the state's institutions in a theocracy, a theocracy is a form of government in which the divine power (in monotheisms the one God) governs an earthly human state, either in person (e.g. as incarnation in a human) or, more often, via its religious institutional representative(s) (e.g. church, temple), either replacing or dominating the organs of civil government as clerical or spiritual representative(s) of god(s). [1]
* Most modern descriptive dictionaries explain that the word is used in most carefully edited texts in English to mean either government by immediate divine guidance (close to the usage described above) or, more commonly, as government by or subject to religious institutions and priests (or a state ruled in this way). In other words, for people who do not believe in a theocracy's religion (or feel that its religious institutions do not represent the religion well), a theocracy is a form of Gleichschaltung that purports to fulfill a divine intention but (since they do not believe in the existence of anything divine or believe this religion is heretical) instead simply fulfills the goals of the ruling priests.
Leep Out: