Note that given the historical existence of the Papal States, the claim is, even when interpreted in the narrow sense, still wrong.
While the donation of Constantine was fraudulent, the donations of Charles the Hammer and Charles the great were real enough, but the church ruled those states under the holy Roman emperor, like a baron under a king - hence arguably not a theocracy. At least that is what they argued, though as the authority of the holy Roman emperor declined, the argument became less credible, and was accordingly condemned.
While the donation of Constantine was fraudulent, the donations of Charles the Hammer and Charles the great were real enough,
The very fact that papal secular authority was justified by the alleged Donation of Constantine reflects a profound lack of theocratic thinking. In a theocracy, a religious leader claims secular authority as inherent to his religious office -- yet the popes and their champions considered it necessary to present their claim as inherited from a purely secular sovereign, despite the ultimate papal religious authority.
I wanted to bring attention to two posts from Razib Khan's Discover magazine gene expression blog (some of you may have been readers of the still active original gnxp) on the polemic surrounding Pinker's The Better Angels of Our Nature.
Relative Angels and absolute Demons (and the related But peace does reign! )
I generally agree with some of his arguments, but found this quote especially as summing up some of my own sentiments: