That statement is not true at all.
I give you that California has about half of Germanys population, but it is not a country. California is a State. Germany is a country and the membership in a political union like the EU does not make it a state.
California (and the other US States) have their own labor laws, their own environmental standards, their own transportation and energy departments, their own distinct safety net programs, even their own militaries! (aka the "national" guard)!
Further, the Federal Government is specifically limited via the 10th Amendment to only those powers which are enumerated to it. By default, legal power is held by the states, not the federal government. This is very unusual.
Every "country" has a different mix of systems and different degrees of local autonomy, but US States are at the very high end of local authority while the federal government is at the low end. Thus, comparing some European nation to the US Federal Government is often misleading as it implies that the US federal government even has the power to do things that a European nation can do, which is frequently not the case, or else is greatly complicated by needing state participation and approval.
I grant you that they are different forms of federal republic, but the point that California is not a country stays the same.
I don't care what kind of power the federal government of the United States has or doesn't have. That is a problem for the US to figure out for themselves.
I don't think that when people compare European nations to the US that they are speaking about the US federal government specifically or imply anything about the power of the US federal government. What is more likely is that they are asking why the people of the USA have not archived what people of other countries take for granted. The fact that this would have to be archived via state or federal government is a detail at best.
These details matter, and they are important specifically when talking about public policy matters and trying to advocate for change.
Back to my original point, there is nothing stopping any US state from adopting universal healthcare, but it’s not clear if the federal government even could if it wanted to (see Medicare expansion and how many states have chosen not to opt in!). Thus if you want to make comparisons to the “things that Europeans take for granted,” it is often more productive to look at what individual US states do and can do, rather than obsess over the federal government. Trivializing that is just a road to getting nothing done.
Geography isn't even consistently taught in the US. Americans don't seem to care about it, they are busy eating their donuts and sipping their mountain dews, despite having a huge GDP and $ per capita... a declining age expectancy that matches third world countries.