The US position - and quite rightly - is "you give up the EU rules, not if you want a deal with me, you got to follow my rules"
The US position as outlined by President Trump is that we will negotiate. Thats it. The Remoaners tried to run with a scare story about the NHS just like they previously tried to run with a scare story about chlorine washed chickens. All President Trump said was everything is on the table in a negotiation and then after the Remoaners tried to make hay out of a completely innocuous statement like that, he clarified the next day and said the British themselves will determine what they are willing to negotiate in any deal.