I find that very hard to believe. Blower vs No has been ask on here dozens if not hundreds of times and if you sift through the responses, the overall theme is " turned my stove from a radiant one-room heater to a convective whole house heat machine"
When you look at the system overall, the goal is to heat the house. The stretch goal is generally to heat the house with as little wood as possible. So the question comes down to: Does a blower get more heat out of the stove and put less up the flue? The common sense answer has to be "yes" for the same reason cars have radiator fans, or you blow on soup to cool it down, or forced air heating is an advancement over gravity feed, etc ...the moving air extracts more heat from the radiator than without.
When you say 'burns more wood with a blower' - one generally thinks of keeping the stove at the same temperature. While that isolated instance may be true, in considering the whole system (and since we know from above we are logically getting more heat out of the stove with the blower) - then it means the house would also be hotter, or the user would shut the stove down more to maintain the same house temp, or the user would put less wood in the stove because a 400F stove with the blower is now delivering the heat of a 600F stove with no blower. In any case, more heat in the house / less up the flue has resulted in less wood consumption, not more.
About the only case I can imagine which would be close, or maybe break-even is a stove in a big, high ceiling room with a lot of exposed single wall pipe. In that instance, a fan might not do much good because the the combined stove+flue pipe surface is enough to radiate all heat possible... sort of like having a car with a swimming pool for a radiator ...no fan needed! Conversely, fireplace inserts benefit greatly from a blower, because the exposed radiant surface is generally very small and/or enclosed in a second / double wall construction and the flue pipe is enclosed in the old FP flue.
