Actually, Michael, I don't agree that the thread you reference explains why there is a Relate/Unrelate button on the Person record.
I am curious about this, too because it's such a pain if we want to move PC's around. We have to go to the person record, then remember or write down the Search Code for the CI, then go to the CI view and reassign the person on the CI form. I don't understand why we can't do that from the Person record. It seems like we used to be able to do that.
We're on SP17 as well, is this something new to SP17?