For those of us without premium, it seems to play the song I request every time...as long as the requests for a single song are at least 24 hours apart. (The window used to seem more like two days, but one day has been working for me lately. Two days ago I played a song around noon, and yesterday when I requested it at 11 it failed, but again at 12:30 it worked. Maybe it's just chance, but it sure sounds like a 24-hour window).
If it's been less than a day, yeah you just get the station and a bunch of "similar" songs. But often if you just skip several songs, it will end up playing the one you want.