Wait so you were playing Skyrim but you didn't buy it?
But yet steam is updating it? Dafuq.
He probably meant something along the lines of 'Didn't buy it so that Steam could update it at anytime due to not having auto-update turned off' I think, not really sure what DC is supposed to mean.
To the OP, Steam will NOT, repeat NOT attempt to update a game while you are playing it and certainly not if you are disconnected.. Since you're using the files to play the game it cannot very well go about updating them. Are you sure it is updating and not syncing the game after you have exited?