Most countries have a legal definition of the "tax resident", which typically is a person who lived more than 180 days last year in this country. No matter if you own or rent property, work or sit on welfare here, it is all about time spent in this jurisdiction.
Having worked abroad (outside EU) for short periods of time I have experienced this, where even owning a house isn't enough to open a simple bank account. But since the EU has specific laws regarding their "common borders" I keep wondering what it would take. I could, in theory, move to any country within the EU and work there, regardless of living there or not. There should be no need to apply for full citizenship to accomplish this, but you may be completely right there, I could end up being taxed in my country of citizenship according to its laws regardless of where the income came from.
Which, for this particular case, sucks.