The part that you quote is a distraction.
This is the poison dart:
""We believe that, under Article II, Section 2, of the United States Constitution, the word Advice speaks to consultation between the Senate and the President with regard to the use of the Presidents power to make nominations. We encourage the Executive branch of government to consult with members of the Senate, both Democratic and Republican, prior to submitting a judicial nomination to the Senate for consideration.""
Yeah. If I'm president Bush, I read that and think, "So what."
He didn't agree to it. The Senate isn't his boss.