I think Amex are less likely to ask for payslips if you are an existing customer.
I would also imagine that their data would still show you as an existing cardholder irrespective of what you type in unless the details are actually different names and addresses.
I would also note that in applying that you
nat000 I think that recent history as recorded by numerous posters on this forum has shown that applicants will receive mulitiple sign-on bonii as long as the type of Amex Award Program (ie Acsent, Gateway, Qantas, Velocity, DJ etc) is different for each card. Many applicants have also indicated that even for the same program that as long as the card is cancelled that they have received a new sign on bonnie. Amex has hinted that this may be toughened up.
What the CSR says can largely be ignored as they will just normally trot out the Amex party line. Such rhectoric does not match the experiences that forumites have posted.
Certainly my experience for my wife and I and other family members is that we have received sign-on on bonii for each and every Amex that we have applied for over the last decade.