False community is the illusion of community without taking shared risks and so being subject to the same constraints, and pressures to agree. Some claim that the risk has to be physical, to the body, not just reputations or ideals. Others claim that it's enough to risk wasting precious time. Either way, it's a risk to become involved in something that claims to be a community, that isn't. False community is a form of false consciousness.
False community is basically an economic concept. It could be considered a question of democratic socialism (arguably a contradiction in terms, since democracy requires the freedom to buy one's own printing press if the collective does not permit the use of its press to disseminate a certain idea; otherwise the political minority, especially a small minority, has no way to make its voice heard, and the system can devolve into dictatorship as the dominant sect of the majority comes to control all speech) versus capitalism. Users are allowed to cast their votes without making any contribution in money. However, they are required to make an investment in time, much as in democratic socialism, people must make the investment of time to go to the polls.
TV Tropes has a slightly different sense of "false community" due to the fact that, despite its non profit status, it is dependent on advertisement money for its existence and admin fiat has a much heavier hand there. For matters that do not concern the economic factors of running the wiki, the community has a reasonably free hand in shaping policy, direction, and goals.
However, anything that would offend the advertisers or the censorship panel known as the P5 (or the TV Tropes administrators) is verboten, and the community has no say over this, nor allowed input, so while they have a community, it has a limited form of freedom in certain areas.
By contrast, communities like Wikipedia have a large amount of community freedom, to the point where they are able to vote on all sorts of issues and shape how community funds (since Wikipedia is a donation-funded wiki like ATT) are allotted, and while funding is required to keep the wiki operating, it has no other controls than that on content or community input.
In short, a community's freedom to decide policy is proportional to how free it is from external factors limiting its ability to function as a true community.