"Pursuit of happiness" is a Creator endowed inalienable right in the Declaration of Independence. I suspect some people confuse that right to freedom as you have described it - as if it meant Christian joy which as you say is another matter altogether, a gift from God.
I wish the inalienable rights laid out in the DofI had been clarified in the Constitution but at least the courts seem to take the Constitution as flowing from the DofI.
That was folish of me. I referred to the Constitution rather than the Declaration of Independence.