There are some details missing. I suspect that the woman moving to Germany effectively moved her out of the Italian health system. Different story if she was traveling to Germany - her Italian health insurance should have been portable then. Moving residence between countries without researching health insurance is not wise. German hospitals will still provide emergency care if needed in a life threatening emergency.

Yes, the German system is not so open. The author correctly describes two options semi-public/private both with entrance hurdles.

The private system are individual insurances. There may be deductibles but generally their coverage is very good. Doctors are paid often double the amount they get from public patients so are also very eager to get these patients. Your health risk here is over-treatment. Why is not everyone getting this fantastic deal? One has to earn a certain amount, be self employed or be a public servant with tenure. The cost depends on pre-existing conditions so unless you enter as healthy&young it becomes very expensive option.

The semi-public insurances are administered by a couple of companies all following the 98% the same rules, some dread disease pool payments between them forced by government to allow portability. Doctors are paid less but the majority of the patients are in this system so there are still penty. Getting a specialist is another topic - there are usually waiting times. The semi-public insurances compete on the 2% differentiation, marketing and their service. One typically enters the public system by not having a private insurance and getting a low paid job. There are other routes to entry but any path less trodden is harder to walk. Unlike the private system the public system covers family (partner if not working and dependent children up to a certain age). Payment depends on your salary up to a limit. In 2017 the MAXIMUM cost based on a rate of 15.7% of ones salary up to a max. salary of 4350€/month are: 317.5 employee and 317.5 employer = 635€/month. If you are earning half then it will be only half.

For anyone in the private insurance the path back to the public insurance is explicitly closed at a certain age. The German system differs from the US system in particular as there is no Medicare. Financing health care in retirement can be a problem for people as the cost in the private system goes up. The private insurances have to put money aside to compensate for health costs of their older customers but that only cushions it.

Health care is expensive and needs financing for dread diseases and high age. This hard fact is a limiting what is possible and requires boundaries to entry. One can not have people saving in one system for a long time and letting others into the same pool when they need access to that pile of money. Germany is able to sustain two systems due to the boundaries between them. The dual system was becoming unstable a few years back when the birth rate decline lead to more older people leaving the private system when older and going into the public one. They enjoyed better service and lower rate in the private system when their health became more costly relied to the wider population in the public system driving up costs there. That was seen as unfair and lead to a shoring up of the boundaries between the two systems.