I think what they're getting at is their custom applications and sites and such that are designed with IE 6 in mind and break when used in newer browsers. However, they have to upgrade eventually because they can't stay on the same thing forever and ever. Internet Explorer 6 was fine when it was released in 2001 but this is 2010, it's time to move on. When even Microsoft is telling you to move on from its own old browser, that should signal something.
There is a cost and in fact, some companies we support here at work require IE 6 for some of their Oracle processing but the fact is, an upgrade needs to be made eventually. As XP and IE 6 get older and older, they're going to become more and more vulnerable and upgrades need to be made sooner rather than later to avoid data loss and corruption. But alas, it's like talking to deaf ears when dealing with these type of people as it's mostly bean counters that make these decisions.