I can think of some reasons why we use
Die Queen in German, but refer to
Königin Beatrix der Niederlande.
Most people in Germany understand a fair amount of English, at least in ex-west-Germany. We say
President Obama as well, for example.
We had a time of occupation were the English language could greatly influence our own, and there is the British national anthem
God save the Queen that is, at least for its title, known to some degree in Germany.
So yeah, if you talk about
Die Queen in Germany, you are talking about Elizabeth.