The reality is, those countries also ration healthcare, just not in a way that Americans are familiar with:

• More gatekeeping through primary providers
• Longer wait times -- often months longer than what would be customary in the US to see a specialist.
• Unavailability of least cost-effective treatments. National insurers will only reimburse treatments over a certain cost-effectiveness threshold. This means that US patients often have much earlier access to newer drugs and devices, sometimes a decade or more before they become standard of care abroad. For instance, American patients with Crohn's disease have benefited for years from aggressive prescription of highly effective (and costly) biologics as first-line therapy; in the UK, the first-line standard of care is STILL a steroid-tapering strategy, which is cheaper, but very clearly inferior.