Well, I take it that he is feeding a baseband square wave into the transmitter's FM modulation input. As AG said, the distortion you get is dependent on several things. The transmitter audio frequency response is the first thing. For square waves of a certain frequency, say like 1000 Hz, you need good low end response down to, oh, maybe about 20Hz or so to keep the tops of the squares flat and not drooping. Also, to keep the edges reasonably straight up and down, you need very good high frequency response. For a 1000 Hz square wave, you would want flat audio response up to more than 20 KHz.
Now, the next problem is that of the bandwidth of your receiver. FM receivers like the one you are using have IF filters that limit your frequency response of the receiver. The wider you modulate your transmitter, the more likely your receiver's IF filters will distort the audio that gets through. So you have to actually adjust your transmitter modulation to as low a level as is practical to minimize distortion of your square wave. Even so, the receiver's IF isn't wide enough to give you much bandwidth, so you are very limited to low frequency square waves, like up to maybe 2 or 3 KHz.