> The Fourth Amendment is part of a document legally defining and describing...

No disagreement there. But that doesn't mean that the document grants the right. It merely recognizes the rights.

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights...

These rights are not granted by the United States. The United States cannot grant or take away natural rights. That's what they are and how they were intended to work.