Yes, they do. It happened to me once, and apparently another poster as well. In my situation, I had an overnight int'l-int'l connection, so my intended length of stay was something like 18 hours. And I was at FUK. An American making an overnight int'l-int'l connection at FUK was an unusual-enough situation that they wanted to see documentation to back up my story.

That's true, but there is a requirement that you answer their questions truthfully. If they have reason to suspect that your stated intentions are not your actual intentions, they may request and require whatever they feel is necessary to satisfy their doubt. In the case of a short or otherwise unusual transit situation, the onward ticket may be just what they want to see to make the situation believable.