The number of people who believe a statement is true tells us little or nothing about its acceptability. Reportive definitions are made by newspaper reporters. A statement can be both a premise and a conclusion in the same argument. If the statement is a conclusion of a subargument, it is both a premise and a conclusion in the same argument. A fallacy is any kind of argument that has a name.
Some good arguments have names too.
Fallacies are bad arguments that have names. A false statement can be the conclusion of an argument. There is probably something wrong with the argument, but it is still an argument. If a premise is true, then it is guaranteed to be acceptable. If we have reason to think it is false, it is unacceptable even if it is true.