And only seem to work on the students of the person who has mastered these special moves?
IMHO, they "work" on those who have been martially trained to avoid impact. If someone prefers to walk into the impact, well, they turn into atemi or 'hard-touch' throws - as Marc outlined further above. In this sense, IMHO again, there is no 'no-touch throw' as a distinct category of throw, just an intelligent reflex response on uke's part to a real threat. (and of course (1) lots of collusive bullshit and (2) some 'mind-stuff' I have not experienced myself but credible sources tell my people like Ushiro Kenji can do it.)
PS: Gornall, please give my regards to Darren.