I have always had cats and lilies. My cats would get covered in lily pollen following me around the fields during bloom (bloom used to be late may to early aug). I threw anthers all over the place not just for hybridizing, we also cut many stems to sell. Pollen got everywhere, all over the ground where they walked. Never had a problem - never had a cat eat any part of a lily. That doesn't mean they didn't damage them on occasion. Imagine -1 chipmunk, 2 cats and a 7 foot Scheherazade stem........
But indoor cats are mentally disturbed (wouldn't you be locked up all the time?) so there could be something to it.
One of my cats "El Destructio Kitty) would actually remove buds from plants just to watch them fall when she was bored. I don't think she ever did that to the lilies but many other plants were targeted. The buds just stuck out there plump and ready to pick. She carefully spat them out, a very picky eater. And we grew many poisonous plants.