“While in Saudi Arabia and other countries they do.”
Rav Moshe issued his psak for the USA, not Saudi Arabia.
Why are people putting all DD into the same basket. DD is a franchise operation. A DD on one block and the DD on the very next block might be owned by two different people, one who misleads people and one who does not. Is there a din “chalav shnisalem min ha’ayin” that one must suspect a switcheroo where there is no reason to believe so? Is it a matter of practice that the coffee pot is washed in the same sink as the dishes the bacon strips were served on, or cooked in? Is this a practice followed in every DD? I know for a fact that this is not the practice at the DD in my neighborhood. When I worked in kashrus, I came across many establishments (usually hotels) that did not wash their coffee pots, or the parts from the machines that brewed the coffee in the same sinks as the other dirty dishes for various reasons (one place washed these pots with the drinking glasses only). If you really want DD and want to be certain about the kashrus of the coffee and everything else in the cup as well, invest $10 on a 4 cup percolator, buy a bag of DD coffee (many flavors have a hechsher), buy whatever milk you normally do, buy any and all flavorings that have a hechsher you are confortable with and enjoy your coffee. Unless you are a rav or a neighborhood posek though, dont go assuring every neighborhood establishment that sells coffee.