The U.S. is an open society. Unlike many other countries, the U.S. does not impose internal controls on visitors, such as registration with local authorities. In order to enjoy the privilege of unencumbered travel in the U.S., you have a responsibility to prove you are going to return to your home country before a visitor or student visa is issued. U.S. immigration law requires consular officers to view every visa applicant as an intending immigrant until you prove otherwise.
No, immigration law delegates the responsibility for issuance or refusal of visas to consular officers overseas. They have the final say on all visa cases. By regulation the U.S. Department of State has authority to review consular decisions, but this authority is limited to the interpretation of law, as contrasted to determinations of facts. The question at issue in such denials, whether you possess the required residence abroad, is a factual one. Therefore, it falls exclusively within the authority of consular officers at U.S. Foreign Service posts to resolve. You can influence the post to change a prior visa denial only through the presentation of new convincing evidence of strong ties.