The value of the US dollar has risen, as valued by gold and by the fiat currencies of countries that are relatively solvent.
The apparent cause of this is not that there has been any improvement in the prospects for the US dollar, but that a chaotic dissolution of the Euro zone looks likely, so traders are switching to the most liquid asset that there is.
Fiat currencies whose sponsoring government have in substantial part a Chilean style retirement system (Singapore, Switzerland, and Australia) tend to behave like gold.
This suggests that were America to adopt such a system, the expectation that gold is likely to become money would cease, and gold would become more like a normal commodity, with the result that it would have a price, instead of being what everything else is priced in, and that price would fall.
Thus if you think that there is a decent chance that the US can get out of this crisis without passing through disaster, investing in assets located in more solvent countries may well be safer than gold.