I still don't think his essay says that. Before the US independence, the colonies were part of the British Empire, with local legislatures in each colony. How did the British Empire manage the 13 colonies without any sort of bureaucracy?
Instead, the essay you pointed to suggests that the bureaucracy existed, but the new Americans were distrustful of it.
How do you interpret the quote "The origins of this, as Martin Shefter pointed out many years ago, is due to the fact that democracy preceded bureaucratic consolidation in contrast to European democracies that arose out of aristocratic regimes." ? It is possible that I misunderstood it (and would be glad to be corrected if I did).
The word "consolidation" makes a difference. Each of the colonies had its own government and bureaucracy, consolidated under British rule. We of course didn't like the policies of the British Parliament, both temporal and ecclesiastical. When we formed our own national government we first tried to minimize consolidation, via the Articles of Confederation, and then when that proved unwieldy we formed the current national government, which started the consolidation.
I know less about the European democracies. Did the French revolution, and return of democracy after Napolean, keep the existing bureaucracies in place? What about after the German Revolution of 1918–1919? I'm pretty sure that they did not devolve power but instead transferred control from the aristocratic regime to the democratic one.
(Post WW2 separation and latter reunification of Germany might be a counter-example. Iceland had local control, then control by the Norway and by Denmark, so might be another counter-example. Perhaps Belgium as well.)
Instead, the essay you pointed to suggests that the bureaucracy existed, but the new Americans were distrustful of it.