I'm not a monarchist but I find the they're not British argument a tad silly. On the maternal side the Liz is from a Scottish aristo family heavily mixed with English aristos. On the paternal side yes she has a lot of foreigners in the family tree but the royal line as such can be traced back nigh on 1000 years or so in Scotland and I dare say England too with in all that time only about three generations not being born in Britain. Sophia of Hanover and her son and grandson! But even at that both Sophia and George I would theoretically have qualified to play at rugby for Scotland as Sophia's mother was the Scottish born Princess Elizabeth Stuart sister of Charles I.   

The name thing is daft too. If someone has a German name because their British mother married a German then they are no more or less British than someone who has a British name because their German mother married a Brit.