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I watched the whole show and really enjoyed it but what jumped out to me was that the audio was different for this audition to others. Listen to it. her voice is pretty much faultless in tuning and timing and sits with the piano arrangement perfectly.
I've got a feeling they took it into a sequencer and corrected the faults, compressed, EQ'd etc. before sticking it back with the video.
I don't doubt she has a great voice, just not this perfect right now.