Well, I would assume they offer healthcare to people who are working or are disabled and not able to work. It's not like you get healthcare in Europe for not putting anything back in the system. Freedom of movement is not a problem in this case.
You are full of it. Germany, for instance, (and other European nations are similar) puts so many barriers in the way of a disabled immigrant that they'll never end up a resident.
You're telling me if I were disabled and could not work I could just move to Europe and live on the healthcare system? That's not at all true.