I must confess I'm not too familiar with the benefits of the UK Platinum Card, but I would be surprised if it provides liability coverage in case you hit someone/something else. Of course you may have this anyway if you own your own car, but since you live in the UK I'm not sure if that would cover rentals in the US or other countries.

I have high limits on my personal policies plus an umbrella liability policy plus I use a Diners Club card to rent (Primary collision coverage) to keep myself covered without having to pay the rental agencies.