is a hot dog a sandwich

Since bread cannot be attached to language in any orientable way, you are right: It ain't a sandwich, it's a salad!

I would find it a tad odd to refer to a hotdog as simply a sandwich, because we have a more precise and common word for it, but I would understand nonetheless.

Not just because of this debate, but also because when you use the ingredients separately you get weiner sandwiches and hot dog bun sandwiches.

It would be odd to call champagne wine, but still understandable. Same for calling a lava lamp an incandescent light. Actually, this would probably work for lots of genericized tradmarks, like jello, bandaid, dumpster, zamboni, kleenex, zipper, velcro, and so on.