Keep in mind that what allows fractional reserve is lack of competition (a company could profitably differentiate itself from competitors by maintaining transparency), and what causes lack of competition is government regulation. In a completely unregulated market, fractional reserve is a non-issue because there is no possibility of monopolistic privilege for any one company or cartel.
You're wrong. What allows fractional reserve banking is the same thing that allows almost everything else in this world -- wealth. Regulation only tries to make sure that the stealing is kept to a reasonable & sustainable level. Without regulation, scammers and parasites multiply 'til there's nothing left to steal -- see bitcoin "investment" for edifying examples.
On a sidenote: Getting rid of corrupt cops doesn't get rid of crime, it only changes the ones who get to commit it.
regulation. Free-market forms of regulation can and will happen, such as agencies whose job it is to monitor firms on their transarency, etc. The difference is that free-market "regulation" doesn't create monopolies, because it cannot create barriers to entry. That means no outrageous levels of fractional reserve - a non-issue.