As other posters have pointed out, the most obvious form of government-ID for non-US citizens is their passport. We don't have anything thing else better, in any case no US-issued documentation.
I have been tempted to try other documentation, ID-card, driving licence, etc., just to test reaction, but decided that it wasn't worth the hastle of trying to explain, even though both my Swiss ID-card and driving licence are in 5 languages, including English