It's certainly at odds with the theory underlying the Declaration of Independence--Thomas Jefferson didn't believe that the government gave citizens the right to life, liberty, and the pursuit of happiness. But of course Thomas Jefferson was in France when the Constitution and the Bill of Rights were written.
I would assume that the earliest White House web site was set up during the Clinton years, perhaps during the second term--it wouldn't surprise me if WJC used it to say something negative about Ronald Reagan or George H. W. Bush, but he probably wouldn't have seen any benefit from doing so.