These systems aren't always publicly available for anyone (e.g. http://ec.europa.eu/dgs/translation/translationresources/mac... is freely available for gov't institutions only, https://www.letsmt.eu/Login.aspx has commercial pricing), but the freely available resources (e.g. EU corpora) tend to be well integrated in the main free MT systems (google/bing/etc).
What you see there is just a bit worse than the maximum currently achievable - you can get a better system for a particular narrow domain (which is often done in practical applications) by integrating domain-specific data and terminology, but for general purpose translation don't expect to get anything significantly better than e.g. google translate even for a small language unless you can invest many man-years of work - e.g. a major funded research project for that particular language.
Regarding "My theory is that it's not that there is anything hard about the language", there are two factors that you must keep in mind. First, the current (pre-neuron) mainstream approach of phrase based SMT works much worse if the target language is highly inflectional, as many European languages tend to be. Second, the main available large training data sets for European languages are mostly legal/government documents, so the systems work better for that domain but much worse on "common" topics since they're poorly covered in training data.
If the European country she is from is within the EU, you can probably get parallel corpus from the EU parliamentary translations. I believe there are other EU research projects which release useful corpus.
Perhaps distribution of the subtitles is illegal under copyright law, but I suspect the trained model would be fine.
It would be an interesting case anyway.
NMT requires massive amounts of data to give even okayish results.