What you heard on Discovery is correct. It has been postulated that the flow of the fluid outer core, and subsequent motion of ions within that fluid is responsible for the generation of Earth's magnetic field and geomagnetic poles. It has also been shown that the polarity of the dominantly dipolar magnetic field reverses, seemingly randomly through Earth's history. I'm not sure of the statistics you mention, but if in fact the average pole reversal period is shorter than the time during which the current polarity has been maintained, you should also consider the standard deviation of the reversals, which is huge. For example, during the Cretaceous geologic time period, there was a long period of normal (or similar to today) polarity known as the Cretaceous long normal. Geologic records show no reversals over this 43 million year time period.