The school was developed well before the 100% DEBT-backed fiat currency we are under now. They have not adapted, and seem to ignore the most obvious problem with this. Money does not just get printed out of thin air! It is loaned into existence! The classic notions of inflation are not accurate when the "debt reserve" keeps sucking money out of existence.
Austrian economics does not only pertain to the US currency. We are not the only currency in the world to have never had hard-backing of our currency. The colonists had the same problem with continental dollar. and the austrians do not ignore the problem of that the treasury does not literally call up bernake, ask for a trillion dollars, and they start up the printing press. The austrians always acknowlege that the treasury issues bonds and the fed buys them, but it is the same principle. Describing that process just describes the little hurdle they have to jump over to print money. It it merely simplifying the language so it is easier to understand.