Finally! I have never spent so long trying to answer a question. I knew you were right, but explaining why was another matter. So, here's what I've found: What you have in the sentence, "Though an American, he has never lived in the States." is called a 'reduced subordinate clause'. From my own mental practicing (running dozens of examples through my brain to see when they set off alarms), and from my research just now, it appears that 'though', 'although', and 'even though' are among the ONLY subordinating conjunctions that can be reduced (meaning without a verb). So, the sentence could easily say, "Though he is an American, he has never lived in the States." However, it doesn't need the verb in FORMAL speaking and writing. Using reduced clauses in informal conversation is probably why people tell me I talk like an old person. :P In short, you are correct, and formal English allows for reduced clauses, clauses without verbs, when 'though, 'although', and 'even though' are used to mean 'in spite of'. As a quick test, rewrite the sentence as such: "In spite of being American, he has never lived in the States." If it works, you can replace 'in spite of being' with 'though'. Sometimes 'though' is used in place of 'but', and in those cases you cannot use a reduced clause.