To me (Brit) _free_ in this context is perfectly understood as _free at the point of use_

By free I mean it's not a direct purchase. I'm perfectly aware that the healthcare system in my country is payed by my taxes.

Medical care in the European Union (in general) is free. Money is recouped by higher taxation on all people, as if they bought into a country-wide policy.

I think we well understand what is meant by "free". It is usually contrasted by the US system in which emergency care is 'free' if you have no garnishable income or property to take.