More than huge statistical bias, I was more thinking that often people pick up and roll dice again quickly when they are rolling dice as part of a series (to-hit, to-wound, to-save for example). I believe that does lead to some results bias just because the dice are not being rolled randomly enough.
For example, think about a D6: if you roll a number, pick it up and roll it again quickly, the dice pretty much travels like a cylinder would. That means that the numbers on the left/right sides have a much lower chance of showing up if the dice doesn't tumble or such before it stops. I think it's why number streaks seem to be higher in wargames, because these sequential rolls with a handful of dice are common.
Having double-numbered dice that roll better helps reduce this effect I feel, as all the numbers should have better chance of showing up in these quicker roll sequences.
Anyway, once again I fear that I may have over-analysed something simple!