I'm sure this will get me downvoted, but it smells like we're missing some of the story here. If I went to the doctor complaining about neck pain and an exam and X-ray showed nothing obviously wrong, and then I went home and didn't seek additional care, why is that the doctor's (or the system's) fault?
From the doctors' perspective: someone shows up at the office complaining of neck pain from _<missing information about the nature of the injury here>_. An X-ray is performed, and apparently nothing is seen that indicates further treatment.
The patient goes home for *3 weeks* during which they apparently decide they're well enough off to go on a vacation.
During the vacation, rapid nerve damage is noted and they seek additional treatment, which they get. Apparently at this point (when the patient's symptoms warranted it), the horrible U.S. healthcare system provided an MRI and the necessary treatment.
Although it seems great fun to preen about the wonders of the NHS and the problems in the US system (where are many), I'm not sure exactly what additional heroics could be expected from either the hospital/clinic or the doctors.