Her point seems extremely muddled. And why she is saying it is another matter.
Still it neatly exposes that old issue of identity. Being British is a political identity, which was formed out of a union of several countries, and then became a worldwide empire. No one ever discusses the English Empire because it never existed.
Britishness is an administrative idea; a political identity. I don't think it has very much to do with tradition or where you were born or indeed where your parents came from. It is ultra flexible.
Englishness, or indeed Scottishness is probably a very different thing conditioned by a way of life, history, and very old attitudes.
That doesn't mean we have to play soy racist games with articles like this.