Cardholders must be 21, not 18. You cannot buy a membership on a child's annual pass either.
Has nothing to do with the ticket. Kids age 10 and older will have an adult ticket. My guess is that if they think you might be under 21 you may also have to show photo ID to buy the membership. (I'm trying to remember if I have had to show photo ID to buy one, in which case they may ask everyone for it)