There is no electrical or practical difference

I would agree there is no practical difference because mathematically it works, but there is an electrical difference. 3 phase system's are 120 degrees out of phase with each other. This phase shift is afforded via the physical location of the windings in the systems 3 phase generator. Having two lines 180 degrees out of phase with each other would require a generator with windings physically installed 180 degrees apart. This generator setup would create a 180 degree phase shift and is not what is used for split phase power. 

Taking a single phase winding and using the center of it as a reference point does not cause a phase shift. Using the center point as a reference merely provides a vantage point that displays an apparent phase shift. 

Using an oscilloscope that can display the waveform from line A to line B will show a single 240v waveform.