Annnnd.....
We have a winner. An educated, historically precise, scholar.
What we know as The Declaration of Independence was published on July 4, as a vehicle to explain to the Colonies, and the World, why the Lee Resolution - originally proposed by Richard Henry Lee of Virginia on June 7 - was adopted on July 2.
So - the true date on which action was taken was July 2, as Dave points out.
But - the PR guys cranked it up on the 4th, and that is what we celebrate.