Those free cards haven't been available for a couple years now.
The reference to a Greyhound ticket number is for Greyhound passengers that specifically purchase a Student Advantage card from a Greyhound depot. In that case they will be issued a Greyhound ticket with a 16-digit number to take over to the Student Advantage website to claim a real agency-issued card to replace the substitute Greyhound ticket/card number.
Amtrak also sells Student Advantage membership cards at staffed stations and will process the purchase in a similar fashion, collecting the funds for the membership and issuing it as a temporary ticket that can be processed through Student Advantage's agency for a card. Strangely, Amtrak passengers must call Student Advantage to process their tickets and Greyhound passengers can still process theirs online.