Man, there is something really sinister going on.
When you search for "Josh Kaufman" in the Windows iTunes application, "Set Fire To the Rain" does not show up in his songs list. It is down below in his Album list, however. I saw a theory on Television Without Pity that the song was incorrectly listed as an album, but if you look at iTunes' underlying API, there is an entry for the song that looks totally normal. So in the deepest depths of their system, everything is listed just fine.
Album: https://itunes.apple.com/us/lookup?id=879954148
Song: https://itunes.apple.com/us/lookup?id=879954149
When you search for his songs using their search API, again "Set Fire To the Rain" does not appear at all, even with a max limit of 200 (he has 19 results total). I can't think of any reason for this. Even if had only gotten 1 download total, it should show up.
When you search for josh+kaufman+the+voice vs. christina+grimmie+the+voice vs. jake+worthington+the+voice, Christina and Jake have 11 results, whereas Josh only has 10.
Can anyone see anything that I missed? It looks like something is specifically blocking Set Fire To the Rain from showing up in Josh's song results, and I don't think it's just that it's the lowest ranked song of the night. I wouldn't be surprised if this gets "fixed" overnight once the damage has been done, so that these claims are harder to confirm. We'll see in the morning! It's getting harder to deny that this show isn't rigged, what with this treatment of Josh, and the plethora of "glitches" Kristen went through.