The UK-issued Platinum card has quite comprehensive emergency medical coverage that covers all expenses when faced with a medical emergency while traveling outside your country of residence. However, as far as I'm aware, the US-issued cards do not provide the same type of insurance unless you purchase an add-on policy for an additional fee. The 'assistance' is merely a referral service. I could be wrong, but that was my understanding.
I have both a US-issued Centurion and a UK-issued Platinum, and keep the UK issued card for the insurance primarily.
Susan