It is not my speciality but my understanding is that if the UK wants extradition of a US citizen it has to present prima facie evidence to the US authorities and that evidence may be challenged in a US court. Conversely, if the US wants a UK citizen they do not have to provide evidence of guilt, merely of charge, and that may not be challenged in a UK court.

I am not aware of their being any grounds other than medical for refusal by the UK of extradition to the US (so long as the alleged offence is an extraditable one).

In short, the US says to its poodle "Jump" and we ask "How High?". Many of us find this distasteful and indeed colonialist, rather as we do many other long-arm provisions of US law.