The Declaration of Independence was signed on August 2. A few who were not present then added their signatures later. What matters is how they intertwine with the events that led up to them, and the consequences they have had for our lives. There may well be much controversy about Columbus' discovery of America but there is less controversy over the fact that Columbus' act opened a chapter in the history of the world that had quite important ramifications. The Declaration of Independence has had a great effect in history, and it is nice the United States has an official birthday, but neither of these ideas is well represented by concern over any fact that a student might or might not know.
Ideas matter more than facts.
The meat of history lies in understanding the motives and behavior of human beings, what they have done, the effects of their actions, and the consequences for the future.