The fix
IE allows you to put specific sites in different security zones under the "Security" tab in the "internet settings."
I stuck the Zone in the trusted section (along with five other websites)--which still has some pretty good restrictions, but lets me loosen them a bit.
Then open the security settings up (dozens of little buttons to pick from), and under "Scripting" click on "allow Programmatic clipboard access." The warning box will go away.