Excuse me? I don't think it was bad advice at all.

Obviously, a dispute is only an option if the OP has acted appropriately and is wrongly being charged.

If the OP cancelled through customer service, and was told at that point that their would be no charge and the certificate would be refunded, then it should be easy to get this reversed by dealing with Hyatt Customer Service.

Hyatt central reservations / CS essentially acts as an agent between the property and guest. Therefore, if the OP was told the reservation was cancelled and there would be no charge, the property has no right to retroactively charge him, regardless of what they say their "policy" is. The blame would rest with Hyatt CS in that case, and not be the OP's problem. It's unclear to me why OP contacted the property directly.