To her, it appeared that you had. That is not a lie, however misinformed it may be. It is a misunderstanding. Nothing more. For the record, I did not think you did.
See, if it was an innocent mistake, why not apologize? Everyone apologizes for innocent mistakes.
No one should underestimate her intelligence SO MUCH as to say “she thought ‘chick’ meant ‘Jack Chick.’” It doesn’t make any sense grammatically, let alone the capitalization. That’s just not a mistake someone makes.