As much as it pains me to say, a hot dog is a sandwich. I can't argue against it. I consider a sub a sandwich, and I think most would agree. What is a hot dog bun but smaller, smoother sub bread? Not an Italian 12-inch but a carb-ish 5 inch. And if I place orthodox sandwich ingredients in a hot dog bun, is that not just a micro-sub? I can put imitation beef between two slices of bread and call it a sandwich, so why no a hot dog bun.
It's indisputable: a hot dog is a sandwich, but it has grown to such a distinct object that it is no longer recognized as such.