When discussing semantics, I believe the etymology is often more important than quoting modern authorities.
...from Latin, fiat "let it be done" (used in the opening of Medieval Latin proclamations and commands), third person singular present subjunctive of fieri be done, become, come into existence," used as passive of facere "to make, do"
One could certainly argue that the 50 coins in the genesis block were created by fiat. Indeed, "fiat lux" is a famous phrase from Genesis, the name alone suggests such a comparison. It is harder however to make that argument for coins mined today. Nobody has the power to issue new coins by fiat, they come according to schedule.
New coins "come into existence" according to a mathematical protocol invented by humans, rather than by decisions by a government of humans.
When classifying the types of currency there is:
commodity currency: eg. gold coins, which have an intrinsic value, that is, they have a use outside of a medium of exchange
representative currency: eg. casino chips, convertible by the issuing authority into government fiat currency at a fixed rate, or gold certificates, convertible by the issuing authority into a specified amount of physical gold.
fiat currency: an object or record that is declared to be money with no intrinsic value.
Unless you add a new classification to the types of currency there are, bitcoin clearly is a fiat currency. "Government" is closely associated with fiat currency, because before the invention of a decentralized currency like bitcoin, it was hard to imagine how a fiat currency would work without a central government to regulate or issue it.
I think the problem is that some people think that bitcoin mining, while requiring real resources to do, is creating something with an intrinsic value. It may model mining of a scarce physical resource, but mining bitcoins makes you a commodity miner like playing "Call of Duty" makes you an experienced combat war veteran.
Again, I think bitcoin is a great invention, but pretending it is not something that it is does it a disservice.