I don’t know about gluten free products, but I know that for a product to be made in a peanut-free facility means even the employees at the factory are not allowed to bring a peanut butter sandwich for lunch.

This is also why many products that seem like they obviously should not contain any nuts will have warnings that they may contain traces of nuts. You never know if a worker has peanut butter sandwich and they have a bit of peanut butter on their fingers when they finish their lunch break and go back to work. You might reply “don’t they wash their hands?” but if you’ve ever tried to wash peanut butter off a knife you’d know how notoriously difficult it is to wash off completely.