The statement is from http://www.celiaccentral.org/myths/:
If it says “Manufactured in a facility that also processes wheat,” it’s not safe for people with celiac disease.
The above is an example of what the FDA calls a voluntary allergen advisory statement. It is different from a “Contains wheat” statement, which is required by law and means that the food definitely includes wheat. The voluntary warning, on the other hand, means that the product is not made with those allergens, but there may be a risk of cross-contact in the manufacturing process. The statement can seem alarming, but in some cases it may mean that the company is going above and beyond to let customers know about their processes.
If you find a product that is labeled gluten-free but bears a warning like this one, you can rest assured because foods with allergen advisory statements for wheat that are also labeled gluten-free must comply with the gluten-free labeling rule. If you’d like to investigate further, NFCA suggests visiting the company’s website or calling their hotline to learn more about their manufacturing practices. It’s absolutely possible for a manufacturer to produce safe gluten-free food for people with celiac disease using shared equipment or a shared facility, as long as they have the proper sourcing, cleaning, storage, production and testing protocols in place to keep the food safe.