I don't buy this line of argument at all. Some people are just inclined to stay between a rock and a hard place. They like it there.

Why does your organization need IE6? I'm guessing because you've got old apps that were pushing the browser envelope by dipping their toes into MS or other vendor-locked APIs. Fix that, and move on. If you're a decision-maker, just do it. If not, you can't really complain about your fate as a modern, paycheck-collecting Sisyphus.