The first insurer I tried asked for a SSN before they would give me a quote, but the second one didn't (and has taken payment/issued the policy, so I suspect they won't ask about it now). Perhaps it's not a strict requirement, or depends on where they are domiciled? BTW, happy to update the thread with who I used once I hear back from AMEX (and/or if anyone wants to know now, happy to answer by PM).
Thanks for this. I think HSBC has enhanced the Relationship Manager offering to the point where their identity is anonymous these days; but I might give the Premier number a call tomorrow and ask.