No, CO allows 1:1 conversion from AMEX points. This can actually be done from the CO website itself. Go into "OnePass Frequent Flyer" > "Tranfer Points into Miles." Then click on Membership Rewards. It's great. As for your other option with points.com, that site seriously devalues miles; you'd get maybe 25% of the amount you converted. I wouldn't suggest it.

If it's oneworld you're looking at, then I think even QF has the same 1:1 deal with Membership Rewards. Best way to look into that is to actually call up their frequent flyer division. I'm not sure on the details, but I did get a round-trip economy fare JFK-MEL for about 80,000 MR points.