How is blood type AB the universal recipient?

No, if you have AB blood, then you can receive A, B, AB, O

Red blood cells of a person with AB blood, would have A and B antigens on their surface. This means that their immune system will not produce antibodies for A or B, otherwise they will end up killing their own cells - all of them, since organs also have the antigens on their surface. The reason they can receive blood from anyone else is because there are only A and B antigens, which their immune system won't attack. O blood type has no antigen, or more accurately a neutral type of antigen that everyone has. So they can also receive O.

You are right; the donor's antibodies will attack the hosts cells, but they don't give the plasma with the cells. Giving plasma is the opposite - AB plasma can be given to anyone, while O plasma can only be given to O.