I've read that thread (although another read-through certainly can't hurt, so I'll go do that momentarily) and it's irrelevant to my question.
In my case... lets say that my site was.... fightinggamereviews.ucoz.com (I realize that doesn't fit the Ucoz url character limit, but it's just an example.) If I wanted to purchase and attach the name 'gamereviews.com' then the domain and part of the existing url would be redundant. I would want to use that transfer method so I could have all my current content at a site named... (fightercritiques).ucoz.com and then I'd attach the new domain name, and it would become fightercritiques.gamereviews.com.
I hope that has helped clarify my issue, and if I've misunderstood anything about the process please by all means correct me.