I don't think that's always true. Expedia has some rates like that. Hotels.com does as well. Those are specifically excluded by the T&Cs.

I think the real determining factor is whether Hyatt pays a commission to the third party, or not. What's actually happening is that a portion of the money Hyatt pays to Expedia is paid to YOU in the form of Hyatt points and benefits when you cut Expedia (and their friends) out of the deal. Even when you pay directly at the hotel with an Expedia reservation, you can bet Hyatt is still having to fork it over to Expedia....

There is ONE honest to goodness third party booker where Hyatt benefits are conferred (that I know of) and that's Costco (www.costcotravel.com). Prive is also an example, I guess, because the agents that book Prive are getting a commission.