Economically speaking fiat is a currency that exists by rulemaking instead of having an inherent value— it's constructed. The definition doesn't say who does the constructing or how.
Bitcoin is a fiat currency— the fiat is embedded in the software that runs on and is enforced by all the Bitcoin nodes, it's the rules that make the currency exist and work. It's largely immutable, participated with by consent, transparent, and cryptographically strong in the way no government fiat is— bit it is technically a fiat currency.
This is no big deal unless you make the Internet-liberitarian/goldbug mistake of thinking fiat is a dirty word.
So, based on that definition, it is true that Bitcoin is not a fiat currency because it is not given value by law or government. However, although it technically does not have a centralized issuing authority that can arbitrarily create Bitcoins, Satoshi Nakamoto did hard code a creation rate for Bitcoin. In a sense, he is the original issuing authority. The only difference between Bitcoin and fiat currencies, when it comes to currency manipulation, is that Nakamoto committed early on to a specific plan for issuing currency. The government (or the Fed) not only does not make that commitment, but it is unable to make such a strong, unbreakable commitment, although it verbally makes similar commitments all the time.
What is a law or a government in any case? Bitcoin is created by rules. The rules are embedded in a program instead of a law-book. The governed users opt in by using the software rather than by living in some geography. The rules are enforced by being mathematically unbreakable rather than with courts and prisons. These factors alone shouldn't be especially significant, other than that they make Bitcoin more just and efficient.
In fact, with respect to money creation there are not a lot of set rules. The main problem is keeping supply matched with demand. From a governmental standpoint demand is usually enforced (at the very least by forcing taxes to be paid in your currency).
In other words, your criticism would be considered a design feature by many economists. Some even considered adding a fee (demurrage) instead of facilitating inflation, encouraging you to use whatever money you had. This would be akin to a 1% asset tax instead of an income tax.
There is also a voting mechanism that can change the Bitcoin protocol, the NSA for one probably has enough computing power and bandwidth to flat out 'take over' the network and give themselves arbitrary bitcoin amounts.
PS: Voting is a basic problem with all network based protocols. If enough machines say this is what happened then that's what happened.
We can argue about whether or not that is a good thing, but let's at least be clear about what we're talking about. Using definitions of words that are different from what everyone else uses is not the way to communicate your ideas to other people, let alone convince them that you're right.
I disagree on many points, but the easiest to argue is that it does, in fact, have inherent value. At its most general, that value is in allowing people to make exchanges they wouldn't otherwise be able to make. In particular, that sadly seems to be centered on drug trade. The fact that someone designed the mechanics has little to do with it.
Back when BTC was close to USD$30, I was wondering how much meat there was to it. I had enough that if the market was going to vanish it would be a damn shame if I didn't cash out (so to speak) before that happened. After a bit of thought I decided to hold on to the BTC. I made a comment to a skeptical friend that "bitcoin can't fail." Then came the compromises and the price of BTC dropped like a stone.
I was disappointed, but I didn't feel like I'd lost my tiny fortune. When I made the statement to my friend, I knew what people were using it for. I was confident they would continue to find value in it and the price would rise once again. My prediction has been satisfied. I don't feel like my confidence was ill-placed, or that I got lucky to see the rebound and no edict has repaired the shaken confidence of BTC traders.
Well, you could say the exact same about every currency. If you are a chicken farmer, it is easier to buy a pound of pork for $5 than trying to trade your chickens for a slab of a pig (i.e. barter). All currencies provide value, since they are a lot easier than barter. The question is not that, it is whether or not they are based on something of inherent value.
There is an online market (of goods) built around BTC because of its particular properties. This market wouldn't exist without it. You can't sub in barter or gold or most other forms of money, and especially not anything that leaves a record.
The nonsense argument about BTC being a fiat currency is confused. There is an authority in a sense that dictates the mechanics (but I see it much like the 'rules' for determining what is and isn't gold.) However there is no authority that confers value of any kind to the currency.