That's the Declaration of Independence, which is a purely rhetorical document. The Constitution itself justifies itself very differently:
"We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America."
And the Fourth Amendment itself, which enumerates the right at stake, specifically talks about "reasonable":
"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
They might talk about "natural" rights in grade school, but that is not the reasoning that the legal system was ever buillt (not even in the 1790s!) to operate on.