Are Burger King's New Fries really Gluten-free?

I've been going through my inbox and reviewing mail that I have starred and have intended to return too. I came across the article about Burger King's new gluten-free fries. In December, the folks at Burger King changed their french fry recipe and then confirmed that their new fry recipe, the first change since 1998, is gluten-free. The new fries are thicker, with reduced sodium and a coating that makes them crisper and keeps them hotter. They have been available in all of Burger King locations since December 5.  

However, I am making this post because even though the company claims that the fries are gluten-free they do warn that their new product may be cooked in the same oil as other products that contain gluten. Burger king has a gluten sensitive menu that can be found here.