yes, that's true. Wood has a primary energy factor of 0.2 (in comparison: gas 1.1, electricity nowadays only 1.8) and thus greatly improves the primary energy demand, which you can then nicely read off in the energy certificate. It has almost nothing to do with actual consumption anymore. How much is needed for heat is more a question of the calculated heating load, which in turn has to do with heated area, number of people (hot water demand), and insulation quality or transmission heat loss.
if you have 500 kg in summer (for what??? - you have DHW anyway) and 1 ton in the transitional month, 2 tons for a cold month is well within range.
I also find that (naively) true. I don’t really understand the drama either.
In the rented house, we scale up 5,000 kWh of gas in warm months per year (only for hot water), in October with heating it is calculated to be over 45,000 kWh. If we actually come out under 30,000 kWh in annual consumption, I am more than satisfied (framework data: built 74, 180 sqm living space, conservatory (fully heated), converted attic)