Actually, I have always considered the Declaration of Independence to be a kind of preamble to the Constitution, and a lot of people have always looked at it in that light.
I presume that Rush was using the word in that sense. The “inalienable rights to life, liberty, and the pursuit of happiness” are basic to what the Constitution says.
So, it’s OK to pretend that the phrase “wall of separation,” which was written in a private letter AFTER the Constitution and therefore had no possible influence on it, is part of the Constitution itself, but it’s not OK to say that this famous phrase about life, liberty, and the pursuit of happiness” amounts to a summary of the freedoms that the Constitution guarantees?
That’s because these documents are all discrete... not some sort of “foundation of government”! What ridiculousness! [/sarc]