Yes. That is quite true. You would need an American side billing address and you would have to arrange for any transfers to pay this account to be made in US$. It's not difficult to do this, just tedious.
One also has to be somewhat careful that you do not use a foreign credit card to pay for goods or services which could be deemed to be UK sourced, otherwise the revenue will be down on you for what they term a 'constructive remittance'. For example, were you to buy an airline ticket in Singapore for, say, a BA flight from London to Johannesburg, you might well run foul of this little twist.