From the article "Rarely during the late 1770s and 1780s was the Declaration publicly read or celebrated. Instead, most Americans celebrated their state constitutions and the promise of liberty contained within them. Or they celebrated their local declarations from 1776."

Though it doesn't say when those state constitutions were enacted, it sounds like the states were already separate things. That would explain the lack of interest in the declaration of independence at the time.

"But Wilson thought its significance lay elsewhere: in confirming that the United States was born a nation rather than a series of independent states."

If there were state constitutions prior to that, I'd say who cares what Wilson thought - facts are facts. Besides, how can you have someone sign from every state if those states are not already meaningful entities? I think a better stance is to say the nation was formed over a period of time, based on a set of principles and ideas (most importantly "we are separate from the old world"). Documents only served to formalize what was happening and agree on how to settle some differences.