The text on the card says “If the Radioactive Potato is on the table it does not prevent victory – instead, you must have the Potato in order to win along with meeting the other conditions of the Goal.”
When playing with a group, some of us read this to mean that you cannot win without the Potato at all, while others of us interpreted it to mean that you can win without the Potato as long as the Potato isn’t on the table AT ALL.
A: The second thing you said: if the Potato is on the table, then you can only win if you are the one who has it. If the Potato isn’t on the table at all, then anyone can win. Otherwise, nobody would be able to win with You Also Need a Potato if the Potato wasn’t out.