How can an FFT plot not be symmetrical?
Using the wav version of the file you linked to I performed an fft in matlab and got:

First 3 terms:

 left channel       right channel
-1.1594 + 0.0000i  -1.8450 + 0.0000i
-0.4186 - 1.0013i  -0.2851 - 1.7655i
 0.5507 - 0.7589i   1.0478 - 0.4655i


Last 3 terms:

 left channel       right channel
 0.7388 - 0.3032i   0.4740 - 0.6654i
 0.5507 + 0.7589i   1.0478 + 0.4655i
-0.4186 + 1.0013i  -0.2851 + 1.7655i


Looks conjugate symmetrical

I wonder if you are processing the left and right channels at the same time and it is thinking it is a 2d signal or a complex valued signal.

The only way you get an asymmetric fft result is if the signal is complex.