Nope, your parent is right, in Austria you also don't get healthcare if you don't work or are looking for work via your local job center.
Maybe France is an exception due to having stronger social system that heavily favors the workers (insert memes about strikes) while in Austria the system is very rigid, designed to favor businesses and the government rather than the workers and to discourage abuse.
I know to a European this might sound like the only two options, but pre-Obamacare, and very possibly again if the US can't get its shit together, it was impossible to buy health insurance no matter how much money you had for a large number of unemployed or self-employed people.
If there are different pricing tiers based on employment status, then the healthcare system is contingent on employment by definition. It's commendable that the American and European healthcare systems aren't contingent on pre-existing conditions, but that's a distinct issue.
Now, yes insurance is expensive, but anyone can get it for about 2x what most people who get healthcare as a benefit are paying into an employer's health care plan.
Not the case in France (at least for the past 20 years), and I doubt it's the case in most other European countries.