Given the persistence of cigarette smell in the body, and the situation in which they ask about the staining, I don't think it's "do you smoke" covertly, but I could be wrong. It could just be that the enamel on your front teeth is more porous, maybe?

I find I get about the same amount of staining whether I drink coffee or tea but that using a whitening rinse before bed seems to keep it balanced out, though it never really improves anything.

Hope this goes well and you feel better quickly after all the poking prodding and prying.