(I’m full of all the grey area answers today.)
It’s easy to think that, if you have celiac, you should avoid anything made in a facility with wheat. But companies are required by law to print that on a package. (And thank goodness for that. When I was first diagnosed in 2005, that wasn’t true.) Does that mean the food you are holding was processed on the same line as flour? Not necessarily.
That line means just that: somewhere in the facility where they made that food, wheat is also present. It could be in a room on the other side of the factory from where your food was made. Wheat could be used four times a week, and one day a week they clean down everything on the line, completely, and run a gluten-free product, but there is still wheat in the facility on some days. And it could be that they use wheat flour on the conveyor belt and there’s gluten on your food.
So you know what have to do? Give them a call. Investigate. If a company will not tell you exactly that that phrase means, don’t eat their food. Most will, however. And those are the companies to whom I want to give my money.