I have read the constitution cover to cover (probably at least as many times as you) and find their job include advice and CONSENT, not just legislation. I find no reference to corruption in the consent responsibility, but I do think rather than corruption, the intent was to limit the ability to appoint cronies to the SCOTUS. And so it should be. Lectures on the text of the constitution which we all can see and form opinions on are no substitute to a reasonable track record which we should be able to examine and test in hearings that would give us some insight into the thinking and commitments of a nominee. The more I see of irrational attacks on folks who want more information on why this person should be confirmed the less I think she should be. While I remain open minded, I'm still not sure she should be but the more heat I get for being skeptical the more cynical I become. Not a smart strategy for those who would win doubters to their way of thinking.
Yes, consent, nowhere does it say that the legislators get to have a say in the procedure other than to give advice or, possibly, withhold their consent. Of course, the founding fathers assumed they would ask questions and not just knee jerk withhold consent without any firm reason other than "feelings".