... Amex subcontracts its insurance. That's totally irrelevant.
I regret if my previous posts are rude, that's not my intention. We simply disagree on our understanding of the contract and on the most effective way to respond.
Have you contacted anyone at American Express who has the authority to change the decision? Explanations offered by front line customer service agents are not a reliable indication of the reasoning which went into the firm's decision.
Have you contacted the ombudsman?