I was under the impression that whatever rules the majority of miners agreed to run on would control the network, hence the concern over a 51% attack.
You misunderstood.
Bitcoin is not a democracy. Bitcoin is a zero trust system. Each full node is autonomous, it validates the entirety of the rules on its own— trusting only its source code (which you or anyone else can audit). Only through autonomy can you have independence and the assurance that the majority of wolves won't vote to have you for supper.
Unfortunately, to resolve to double spending a digital cash system must have a way of agreeing what order the transactions happened in. Its is not possible to have a decentralized antonymous system where everyone agrees on the same order of events— because the apparent temporal ordering of events depends on the relative position of the events and the observers in space— this is a consequence of relativity. So before Bitcoin many people believed that this sort of system was fundamentally impossible.
Bitcoin solves the fundamental impossibility by relaxing the autonomy by the minimum amount necessary: We use a majority of computational power to decide on the ordering of transactions. But _ONLY_ the ordering. Nothing else. That one compromise makes all the rest possible.
Of course, controlling the ordering of transactions is a powerful thing— because a transactions validity depends on its order relative to possible conflicting transactions penned by the same author. This is why it's important that the majority of the Bitcoin computing power is well distributed, that we don't let it consolidate into the hands of a few service providers (like mining pools or exchanges). The use of computing power makes the the system not only resistant to attack, but it makes the attacks have a clear and fairly consistent real monetary cost— so people can reason about the risks, and the economics of the system make it so that it should hopefully be more profitable to cooperate than to attack it.
The state currencies of democratic nations is theoretically democratic money, unhappiness of the current state of affairs is part of the motivation behind Bitcoin. Democracy is not a good method of making decisions— it's often just the least bad option. But Bitcoin is something stronger than democracy, ... though not quite as strong as the laws of nature.
Of course— the rules of the system can be changed, but it requires basically everyone to agree to the change because the old system and change system won't talk to each other, it's basically like replacing Bitcoin with something else. This has actually happened, for example, there was once a bug in the rules of the system where the values of transactions could overflow and someone exploited the bug to create a billion bitcoins for himself. People noticed this right away and published a fixed version of bitcoin which rejected the block containing that transaction and all blocks after it... and everyone applied the fix, because it was obviously in everyone's interest except the attacker's, and life went on.
But if people are afraid of e.g. the supply of Bitcoin being changed they really shouldn't be. Yes, almost all the Bitcoin users could switch to some fork of bitcoin that had different rules— but with the same effort they could just switch to paypal. There is always the risk that someone will use something else. But Bitcoin itself isn't subject to petty majority rule.
(I wrote basically the same thing at
https://bitcointalksearch.org/topic/m.723476 too ... couldn't find it at first because the only quote I could think of from it is all over the internet now
)