Just as the title says. Made a game with Lord Rattington, and it said I didn't own any non-Base cards.
This is a known issue, it also happened to me. Refresh the page and log in again. Then you will own all cards.
No, I can play with all sets against human players, but playing against the bot restricts me to only Base.
EDIT: Hmm, just checked this morning and it seems to have been fixed.