We do this in person too, not just with celebrities, to a different extent. We do this with people we work with; we only see a small part of their lives and we sort of create an identity for them that's "more whole" than the pieces we have actual knowledge about, but very little likely basis in, you know, fact.
In terms of all of us here, all on livejournal, we do it with each other even if we aren't celebrities. I'm not a celebrity, but I'm sure there are persons on and about livejournal that have an idea of the person they think I am. But we're only sharing small bits of our lives with each other.
You're sharing smaller and more frequent and more limited bits, maybe, with much larger groups of people, and it's not even necessarily a shared community (like, say, my friends list, or the social media task force I'm working on with the ABA). So the "construct" of you is more tangible and distinct, and certainly more present in your life, and likely far less accurate, than it is for folk like me who aren't famous.
I think it's generally helpful when dealing with people--big celebrities, small celebrities, people we know only from a particular context--to remember that they are whole real people that we really don't know anything about.