AVPlayer rate property does not work?

Confirmed. I actually had a ticket with Apple DTS open for this issue and a bug filed. The only supported values are 0.50, 0.67, 0.80, 1.0, 1.25, 1.50, and 2.0. All other settings are rounded to nearest value.

The play rate restriction appears to be due to pitch correction, which is now configurable in iOS 7 or later.

// This prevents the play rate from going below 1/2.
playerItem.audioTimePitchAlgorithm = AVAudioTimePitchAlgorithmLowQualityZeroLatency;

That seems to be the default setting:

Low quality and very low computationally intensive pitch algorithm. Suitable for brief fast-forward and rewind effects as well as low quality voice. The rate is snapped to {0.5, 0.666667, 0.8, 1.0, 1.25, 1.5, 2.0}.

The other three algorithm settings let you vary the play rate down to 1/32. For example, AVAudioTimePitchAlgorithmVarispeed turns off pitch correction.

// Enable play rates down to 1/32.
playerItem.audioTimePitchAlgorithm = AVAudioTimePitchAlgorithmVarispeed;