Why does my AirPlay stream distort at high volume?
Network issues only ever result in the audio cutting out, they can't really change the content.

Distortion means your speakers get overloaded. Turning down the volume is your only option.

The reason your speakers are fine on the Mac is that after the slider in iTunes the sound gets further attenuated by the system volume buttons on your keyboard. If you turn those up far enough you'll get distortion as well.