Is G-d required for democracy?

At a graduation I attended recently, the keynote speaker suggested that, in societies where most people follow all of the laws all of the time, human societal obedience is based on a fear of punishment. This punishment can come from either a human dictator or G-d. He further suggested that, in order for democracy as we understand it to work, the society must be predicated on the latter, even if that society has drifted (for better or worse) from its faith-based roots, e.g. the United States.

He further posited that dictator-based societies upon which democracy is imposed from the outside tend to break down rapidly. He used Haiti as an example of this; ousting the Duvaliers, as bad as they were, did nothing for Haiti's political stability, and the country still struggles today.

This is, of course, a simplification of what he said, which must in and of itself be a simplification of the concept; I'm sure tomes could be written about this, but he had to fit it into a small part of a graduation speech. A quick Internet search does not reveal that he's written about this, but I'll see if I can't find something more in-depth later.