Who Stole the Tarts? Part III

"Well, here is your flour," said the King happily, "so now you can make the tarts."

"Make tarts without pepper?" asked the Queen.

"Pepper!" said the King incredulously. "You mean you use pepper in your tarts?"

"Not much," replied the Queen.

"And I suppose it was stolen!"

"Of course!" said the Queen. "Find the pepper, and when you have found out who stole it, then off with his—"

"Now, now!" said the King.

Well, the pepper had to be found, of course. Now, as you all know, people who steal pepper never tell the truth.

"What!" said Alice (not the Alice in Wonderland, but the Alice of this party). "I never heard that before!"

"You haven't?" I said in mock surprise.

"Of course not! What's more, I don't believe anybody else has either! Have any of you heard that before?"

The children all shook their heads negatively.

"Well," I said, "for purposes of this story, let's assume that people who steal pepper never tell the truth."

"All right," said Alice, a bit hesitantly.

So, to continue the story, the most obvious suspect was the Duchess's cook. At the trial she made but one statement: "I know who stole the pepper!"

Assuming that people who steal pepper always lie, is the cook guilty or
innocent?

(Source: Alice in Puzzle Land: A Carrollian Tale for Children Under Eighty by Raymond Smullyan)

This one is simple, if an assumption not explicitly included here is added. Suppose that the Duchess's cook is the thief. In addition, assume that the thief would necessarily have full knowledge of the commission of the crime. In this case, the cook would have said that she didn't know who the thief was, as pepper thieves always lie. With this assumption, we can then conclude that the cook was not lying. Of course, even outside of Wonderland, there are instances where an individual may have no memory of a heinous crime:

Taken from Phencyclidine Abuse and Crime: A Psychiatric Perspective (Bauman and Bauman)

...but including this assumption expressly might have made the answer too easy to figure out.