The square wave doesn't work as an example. It's symmetrical and repeating waveform, both polarites gives the same end result. Try something with a more transient nature, like this drum track:
andreaslupo_snurresprett_snippet 1644.wav
Since the ear is mostly deaf to negative transient events, flipping the polarity sounds like a transient softener on this track. Transient on, transient offs. The snare gets a lisping quality to it with the polarity inverted and the overall sound is duller.
Inspecting the leading the edge of the drum waveform confirms that the initial blast is moving in the positive direction. If this track had been sent to mastering as an inverted file, flipping the polarity would be a very quick and easy way to get more punch out of the track.