It can be cheaper to book on a 3rd party site every so often. Travelocity had a fare that was literally $300 cheaper than anything else I could find for a flight to Europe in October. Odd thing was, the fare didn't show up directly on Travelocity either; it only showed up as a "We found a cheaper fare for your dates" option after I went through and selected dummy flights for my dates.

I have no real evidence, but IME it seems like this is more often the case when booking a ticket using multiple airlines, even within one alliance.