I researched this last year when planning a RTW trip. I approached Amex and received the following response which should be noted:
Kindly also be informed as to how the travel insurance is activated:
Activation of Transport Accident Cover (Section A), Card Account Balance Waiver Cover (Section B) and Travel Insurance Cover (Sections C–K):
Cover is effective for each Trip only when:
(a) You pay the full fare for a return Trip on Your American Express Platinum Card; or
(b) You pay using American Express Membership Rewards points, frequent flyer points; or
© You use Your Travel Benefit.
The Trip must be a return Trip and commence and end in Your Country of Residence. Cover is not activated until a return ticket has been purchased.
Important: One-way Trips are not covered.
The activation of the insurance is purchasing the full amount of your fares departing and returning to Australia as well as any internal transfers within Australia using your American Express Platinum Card or with American Express Membership Rewards points, frequent flyer points or with Your Travel Benefit or a combination of those payment methods. There is no expectation as to the cost of the fares just as long as 100% of the fares (including the taxes) that you are required to pay to have been charged using one of those payment methods.
Booking with your Frequent Flyer Points will only work if every single point used was converted from your American Express rewards points, otherwise, it will not activate the travel insurance.
Please be advised that the travel insurance only extends to any Platinum Card Member which means:
1. the person who is issued an American Express Platinum Card as the primary account holder or a supplementary or additional Card Member; and
2. their husband, wife, fiancé(e), de-facto or life partner with whom they have continuously cohabited for a period of six (6) months or more; and
3. their legally dependent children (including stepchildren or legally adopted children) who are twenty-four (24) years of age or less and wholly dependent on them for financial support.
Any customer who meets the above definition may use the same travel insurance benefits and may lodge a claim in the event of a loss. Please be advised that all claims will be subject for assessment by the Claims Department on a case by case basis.
In my case the points used were not earned through Amex Rewards so the insurance would not be activated. I had to find insurance elsewhere which was 1Cover.