Authorized users (or additional users) don't need SSNs since they are not the PRIMARY account holders.

What support/sustain the cats'/dogs' cards are the credit history of their masters (such as you and Bidkat), the primary cardholders, who have willingly added the pets to their own credit cards as authorized/additional users. (And swipe the credit cards on their pets' behalves. )

As for your friends who can't even get their own cards, I can only say your credit ratings obviouly outnumber them. If you like, you may give them a helping hand and add them to your cards as well. Be aware though. Your friends might not use the cards as "responsible" as your dog and your credit could be dented as a result.