Based on the Austrian approaches to property rights and the title transfer theory of contract (Rothbard, Evers, Hoppe, Kinsella):
You are very close to the truth so let me help you get all the way there.. If I counterfeit money is it not fraud if I tell everyone what I'm doing (if my counterfeited notes indistinguishable from real notes)?
It is not fraud similarly as copying is not fraud if the buyer knows it's a copy and the seller does not misrepresent it. If the concept of IP is invalid, as Kinsella argues in Against Intellectual Property, then creating "counterfeit" money is also not fraud. Manufacturing of "counterfeit" money does not violate anyone's property rights, unless the material used in the process was stolen. Passing the result while misrepresenting it's context, however, can be fraudulent, similarly as trying to sell a photocopy of Mona Lisa while claiming it was painted by Leonardo (except noone would fall for this one).
FRB robs savers by lending money to borrowers that doesn't exists effectively transferring purchasing power from savers to borrowers without their consent but not only that the bank also artificially increase the supply of loans which lowers the available interest rates on loans even further punishing savers. It's fraud, disclosed in a free market or not.
In the Austrian School, there are no property rights in values (see Block, Hoppe, Kinsella) or purchasing power, even though some of the Austrians use the redistributive element of FRB to argue it's illegitimate. I maintain that in the absence of legal restrictions, the redistributive effects of manipulations of the money supply are an externality, since the act of A creating more money, or even the act of B and C using this money in trade has no effect on the physical integrity of the property of another guy, D. Similarly as if I figure out how to create oranges out of nothing, the other producers would take a huge loss even though their property rights were not violated. The only exception is in case of legal restrictions, for example, if A has a monopoly on production, or if he can force D to use the money in some context.
Yes, but who would take a note that has on it the disclaimer that hey: "This private promissory note is redeemable for 10BTC oh and btw we might print way more than we actually have reserves of, hold it at your own peril!" I can't imagine people willing to receive payment with such a financial instrument if it can be called that at all.
This can be disproved empirically by showing substitute money which is not a legal claim. For example, mutual credit, which is pegged yet there is often no direct convertibility. Even Mises argued that there is no requirement that money substitutes have a foundation in legal obligation, it is sufficient that they are functionally exchangeable.
The reason why people accept all kinds of instruments in payment is that they provide something which the original does not. deSoto mentions, for example, ledger keeping. Gold does not have a ledger, and if someone wants a ledger, this can shift his order of preference so that even riskier instruments (e.g. fractional reserve current account) rank above gold.
Edit: furthermore, since substitutes which have reserves are associated with costs (e.g. storage), the issuer of them needs to compensate for this somehow. He can charge the users (e.g. demurrage, transaction fees), or he can use the reserves for some other purpose (e.g. loans or financial markets). All other things being equal, a user would choose the one where he does not have to pay. This makes a full-reserve unlikely on a free market. If there is a demand for substitutes, the market forces will lead to fractional reserves.