Anything can happen in a store owned by a non-jew. For example, they can bring their ham lunch and eat it on their counters and use the same utensils for their lunch as your food! They don’t see what’s wrong with it after all they don’t agree with your religion anyway! Also, there are always stories of cleaning woman that treif other people’s kitchen when owners aren’t looking. A goy is not trustworthy as a general rule when it comes to kashrus. There may be heterim for such an establishment, but I am in awe at how people are desperate for DD when there are other better hechsher establishments out there. BTW, I eat OUD and still won’t eat in DD. The hechesher generally creates a fear that they can be inspected anytime for kashrus compliance. Everyone knows we don’t come around on Shabbos and inspect unless some Kashrus org. do in which I am not aware of.
