QE2 was absolutely right in rejecting her as Duchess to Harry. Markle is a dog, a chihuahua even, in a pride of lions.
She hasn't worked out as an American of the natural aristocracy for the same reason, and never can. She does not have the true sense of personal independence that is accountable only to God Almighty that rises above man-made "nobility."
Her father is descended from a knight in the realm of Henry VIII, and he has many blood connections to early colonial New England families.
She didn't reject her; far from it. She gave them the Duke and Duchess titles and has not taken them back in spite of many calls by the British citizenry to strip them of their titles and remove them from the line of succession.
What the Queen did do is order them not to commercialize their titles, as they had planned to do by using it as a brand on merchandise. This is standard Crown protocol for all royals.