The arithmetic mean and geometric mean in the CPI calculation

Aha, the damn BLS bureaucrats have rigged the CPI calculation to help the Fed and Obama. They changed the formula for the CPI. When? 1999. In 1999, the BLS must have anticipated the economic crisis, Obama's election, and the Fed QEs since 2008. What a surprise!
Besides some non-factual criticisms, such as "prices of oil and food are excluded" or "rental equivalence lowers the CPI", what indeed interests me is the introduction of geometric mean that replaced arithmetic mean in 1999. By the way, prices of fuel oil and food are included in CPI calculation and rental equivalence actually has tended to raise the CPI. Crude oil price is not included in the CPI because we do not consume; housing prices are very volatile compared to rents, so rental equivalence has had an effect to raise the CPI overall.
Anyway, regarding arithmetic mean and geometric mean again. An arithmetic mean is what we usually call an average. It is the summation of all observations and divided by the number of them. A geometric mean is the n-th order root of multiplication of all observations. Mathematically, it is true that an arithmetic mean is always not less than the geometric mean of the same observations. In that sense, the BLS critics may not be all wrong. However, their arguments seem to be based on misunderstanding.
Let's imagine that I purchase 10 cheese burgers every week. There are five brands: MD, BK, AW, W, and DQ. Initially, they have an identical price, 5 dollars. They are close enough to be considered perfect substitutes. All of sudden, MD raises its price to 6 dollars while the other brands do not. Then, I will buy 10 cheese from the other brands. My consumption per burger is still 5 dollars. However, the arithmetic mean price of cheese burger will be 5.2 dollars. The mean price is skewed as much as 20 cents in this case. If we take geometric mean, it will be about 5.19. It is still skewed but better than the arithmetic mean. Since perfect substitutes are hardly observed in real life, the geometric mean price likely captures substitution effects much better.
Actually, computing geometric mean prices into the CPI has lowered the index about by not greater than 0.3%, according to the BLS: http://www.bls.gov/opub/mlr/2008/08/art1full.pdf
Isn't it quite different from Internet conspiracy theories?