If the OP is 100% certain that they or the travel agent never canceled the reservation they have a case IMO.
However Hyatt at some point should be able to fully trace down the res trail at some point and look at the history as who how when & what..............
If central reservations canceled it who was the party who canceled/authorised it?They always check details/ information before canceling

It is at the very least a broken contract. That is if Hyatts at fault and the OP or the travel agent wasn't in anyway the the cause of the problem or had anything to do with the cancelation......

If it were me and the fact was I had nothing to do with the issue its enough to cancel all my future business with the chain without a reasonable good will gesture equal to a walk policy.......

Unrelated or related Hyatt has some serious problems internally with information management.
Hyatt.com also has the most serious problems IMO of any hotel website with repeated technical and systemic failures .....
These comments above have nothing to do with which hotel website I like better its about having a functioning site.
I like Hyatt.com but its being managed very poorly and for far too long
Perhaps off topic from the website
Last week a number of my upcoming reservations couldn't be found on Hyatt.com
Either an agent.the hotel or the system kicked my GP number out of the system on numerous reservations
Now I booked them online and had all the confirmations with my GP number on all the bookings before they self destructed