Actually I got an email first, then went to status checker and it had the admitted students' site link. From what I've heard on the board, it means you're in.
You should just call Cornell and be like "It says admitted students' site... does this mean I'm in?" (And they'll tell you yes). I did that with Vanderbilt because I got ASW info before my acceptance... and they affirmed over the phone that I was in.