I’m thinking that Fergie considered this as her job much as Kate, although a Duchess is called a “Princess of the United Kingdom”.
However Fergie was divorced a quarter of a century ago Her only access to the RF is through the girls.
A Duchess isn’t automatically a Princess, but if you marry a Prince, you are a Princess by marriage (like Kate, Meghan, and Fergie was)
But that’s not he reason she said it... she was rushing to get somewhere and had just been asked if she was Queen. She was trying to bring the conversation to a halt... it looks like so she didn’t miss Eugenie leaving.
m.youtube.com/watch?v=3WWSgHqzS7c