You're right, my favorite politician, that libertarian from Texas, Ron Paul said it. I love that guy....
The dollar's influence today, and its precarious status as reserve currency, has more to do with Asia's export-driven growth strategy (see the article Gavin linked to) than the petrodollar issue, though it will certainly speed the demise of the dollar as international reserve currency as Russia, Iran, et al, price oil in euros. I also believe the US (administration) is more interested in controlling access to oil than maintaining its price in $s.
As for the euro, there is an increasing demand to hold non-dollars as reserves by central banks, and the euro is the only other (real) option until China opens up its financial markets.