Most hotel chains do not consider Expedia bookings as acceptable rates. That being said, I think that is a load of crap. If you can book the same rate on Expedia that you can on Hyatt.com (or said hotel chain's website), then it should be a rate they accept with full credit. Expedia, Travelocity, Orbitz, etc. are not like Priceline. Many of the SAME rates (government, AAA, etc.) can be booked on Expedia and Travelocity as can be booked with Hyatt. When you can book the same rates, not bare-bones Priceline and Hotwire type rates, they should count regardless of where they're booked. Even the airlines see that and give full mileage credit for these sites.
When Hyatt decided to make its rules more strict, I think they went overboard. I also think the same of every other hotel chain that does not honor online bookings made through Travelocity, Expeida, et. al. It is one thing to say a $39 room at the Grand Hyatt Atlanta booked through Priceline doesn't count, but it's totally different to say that a $139 AAA rate booked on Expedia doesn't.
There should be a happy medium somewhere. Expedia and Travelocity are travel agents afterall. That is a profession airlines and hotel chains should respect because it brings them business. I know I'm cranky today, but some bean counters in the back rooms are taking the whole eligible rate thing too far. They should look at rate type, not where it was booked. If a AAA rate counts at hyatt.com, then it should count regardless of where it was booked.