I hear this line "first is checked in full" constantly now it seems. I don't know what it means either. On a recent code-share on NWA from DET-CLE they told me this. I boarded only to find that 7 of the 14 seats were EMPTY. And they stayed empty after the door closed. I glared at the FA from my bulk head row in coach and she finally let me come up.
Last weekend in Seattle, we were told the same story for SEA-EWR. I was already upgraded but wanted to take my companion. I always say "even though it is 'checked in full', can we get on the list anyway?" They ended up selecting us as the 'random' pax to wand. I asked again about the upgrade after going through this ... when I took my seat I saw two empty seats in FC and they did let him and another pax come up to take them. So I have no clue. I think it means that either First IS checked in full, or they just don't want to bother with us.