At the risk of belaboring the obvious, one reason the Declaration of Independence refers to certain rights as natural rather than constitutional is because the CONSTITUTION DIDN’T EXIST YET.
The Constitution gave formal, legal status to ideas that had been expressed many times before, including in the Declaration of Independence. There was obviously some pre-existing basis for the view of individual and collective rights incorporated by the framers into the Constitution. The framers’ collective vision of rights wasn’t a sudden revelation like Paul on the road to Damascus, after all. It was in fact based on Enlightenment era ideas and philosophies that had been under development for centuries.