I believe that this whole business about Kate knowing (or believing to know) who the Ripper was is a myth.
There would have been scores of people in the neighbourhood who had theories about the Ripper's identity .......
"Everyone has become an amateur detective here, and the favourite pastime in train, in bus, and in the streets is to endeavour to find one's ideal of the unknown miscreant."
Freeman's Journal, 3 Oct. 1888.
"Everybody has a private theory of his own with regard to these crimes, and naturally I have mine.....
In the railway, on the tram, in the omnibus, at the restaurant, in the street, everybody looks at everybody else, and wonders if the other man is the Blanca Cappella Assassino."
George R. Sims, 7 Oct. 1888.