You are correct, and it is indeed good to make this clear. I meant to argue that it is a bit of an exaggeration to say the the EU has nothing to do with universal healthcare. Arguably, I have more rights to health care as a EU citizen visiting another member state than a US citizen who can’t afford health insurance. Furthermore, it is unlikely that a state without socialized healthcare such as the US would be able to join the EU without reforming its public health policies.