"What transpires now, Miss Marple,
is official business to which you are not invited."
Stuart McMillan and Jane Marple both exist in Earth Prime-Time. Miss Marple, in fact, has counterparts in several TV dmensions (not to mention in BookWorld and the Cineverse!)
For Earth Prime-Time, Miss Marple is portrayed by Dame Joan Hickson.
But her exploits were chronicled by Dame Agatha Christie in a series of books and short stories which became famous around the world. And they are written in such a way that many readers don't even realize she was this little old lady who once lived in the village of St. Mary's Mead.
Whether or not Commissioner McMillan knew through his police work that she was a real person is irrelevant. The point was only to prove that this was not a Zonkable offense.