I don't know anything about the "River Creek Improvement District" but it makes sense to me. There's no reason a corporation cannot buy a section of land and be given the authority (by the State and/or County) to regulate that property as they see fit. However, the ability of the corporation to regulate that property is still limited by the scope of State and Federal law. There is no possible way for them to change, for example, the (general) criminal laws that apply in their area. Murder is a crime under both Federal and State law. There is no place under US jurisdiction where murder is not a crime. Since Federal and State laws regulate almost every important aspect of life, about the most 'freedom' you would be able to get out of such a community would be control over your own local finances, local taxation, local statutory laws, and possibly some aspects of 'bigger' things like building codes, depending on the laws of the State you are in.

Even if you were to somehow able to get the State to grant you independence, so that you are not covered by State law, you would still be covered by Federal law. Federal law covers all US territory, from the actual USA itself, to territories, possessions, embassy property, and some cemeteries on foreign soil. The only places where Federal law has limited jurisdiction are US military bases, but even that is hazy at the moment. The issue of Federal jurisdiction over military bases is a major part of the Guantanamo controversy.