...There is something wrong with that statement but I can't... figure out what that is.
Simple, a sandwich is sideways, while a hot dog faces up.
But no because of open-faced sandwiches.
The statement is still wrong, but not because of that. XD
I'd say that they're somewhat akin to wraps.
Of course, the hotdog itself does not qualify as a sandwich/wrap until it has been placed within a bun.