Stumped by keeper's pads

"A fair delivery was trapped in the top of the wicket-keepers pad.
He removed the bails with the pad that had the ball inside with the batsman just out of his ground but not attempting a run. A not out decision possibly? In Tom Smiths Law 39 page 243 (bottom of page) it states: Provided the striker is not attempting a run, the ball does not have to be in the hands of the wicket-keeper in order for a stumping to be achieved.
An out decision possibly? Can you throw any light on it?

Lots of theories were put forward after the match but I am still not sure which decision is right ."

Law 28.1 tells us that, apart from any actions of the striker, the wicket may be put down by the ball, the hand holding the ball or the arm of the hand holding the ball. Therefore, in the case quoted, the wicket has not been properly put down and the correct decision is Not out. The meaning of the comment in Tom Smith's is clearly explained in lines 1 to 4 of page 244 of the book, lines that follow immediately after the sentence you quote. There is also further useful comment in the rest of that page.