But these people are largely hired and paid for by the government. The government, who has to pay extra if inflation goes up (esp. in Europe). Obviously they have a preference for lower inflation.

(and frankly, to a small extent their argument is valid. If everyone switches from Coca-Cola to Pepsi, even if they do so because it's cheaper, then Coca-Cola has no place anymore in an inflation index. Prices are meant to affect buying behaviour and products must be allowed to replace each other)