Elizabeth I?

I was reading a biography of Queen Elizabeth I, and I am confused about something the author says. The author is talking about Blanche Parry, a member of the household staff. I quote: "...and it is assumed that it was she who taught the great-granddaughter of Owen Tudor to speak Welsh."

The author does not include a family tree and does not discuss Elizabeth's lineage other than her father. But I count five generations from Owen Tudor to Elizabeth, not four.

If I remember correctly, Owen Tudor married Katherine of Valois (widow of Henry V). Owen and Katherine gave birth to Edmund Tudor, who married Margaret Beaufort. Edmund and Margaret gave birth to Henry VII, who married the daughter of Edward IV (another Elizabeth) and sired Henry VIII.

That would make Elizabeth the great-great-granddaughter of Owen Tudor, not the great-granddaughter. Did this historian get the family tree wrong, or do I have my Tudors mixed up?

I had an interesting conversation about 8 years ago with a visiting Scot. He confirmed for me that in Scotland's eyes-if you are born on this side of the Atlantic, you're not a Scot you're a yank.
That's always been the way I've thought of it.
I don't wakl around saying I'm Scottish, irish or Welsh when I'm not.
I'm an American. I don't even use Irish American or Welsh American. American should be all that's needed on the subject.
But two years ago, I talked this over with a student who had spent some time in Ireland and she said the opposite. That Irish Americans are regarded as Irish (or very close to Irish) in some parts of Ireland.
So I have Welsh, Scot, and Irish in my family tree. All cultures from the British Isles that are not actually Britsh are represented in my blood.
What do the Welsh, Scots, and Irish have to say on the subject?