Maria Luisa will be OK, but not having had health insurance is indeed a common problem for European / EEA citizens applying for permanent residence status in the UK.
In this article in The Guardian: https://www.theguardian.com/uk-news/2016/dec/30/spanish-uk-resident-fears-insurance-loophole-will-force-her-to-leave , a Spanish national, Maria Luisa, was worried whether she would qualify for permanent residence status in the UK (such applications are very popular at the moment due to the uncertainly over Brexit). She has been living in the UK for the past 16 years and is married to a British national. According to this article, Maria Luisa was worried that she took some time off work, approximately a year, when she had a child and returned to work 4 years ago; she has been working since. The main point here is that European / EEA citizens do not just get residency rights in the UK beyond the initial 3 months (as it is widely believed). Instead an EEA citizen is expected to be exercising Treaty rights, such as working. Those who are not working can be classed as “self-sufficient”, and this includes EEA nationals coming to the UK to study. ...