No. The primary card holder is responsible for any debt racked up.
Just be aware that sometimes amex does checkI like getting these ones because they are so easy to satisfy. My kids never see the cards and soon I'll add the dog and cat.
About 2 years ago, I got all my plat edge supps including primary audited, they asked for my Id, pay slips and bank account
And ids of all my supps.
I was able to provide all but one because one was overseas and thye cancelled that
Funny thing is 3 of them were all me, using variations of my first and middle name
Eg. Mike John, John Michael, Michael, John
I supplied all different ids of the same person eg drivers license, passport, Medicare
And they weren't cancelled
That being said I received a letter from amex on April 23 asking for the same for my explorer.
I did the same docs and haven't heard back and am a little bit too scared to call up since this time my docs weren't certified,