Agree; "they" was in reference to the property, not the issuer; have edited to clarify. This discussion started in the context of a bad faith insistence by a property on wrongfully passing along costs to a consumer who was not liable for them, even after being notified of the error. Certainly that's more in the neighborhood of "fraud" than a truthfully initiated chargeback; although I suspect it'd be an uphill climb to show that either meet the threshold for fraud in a legal sense.

Yes, I can always sue the hotel, and yes the hotel can always sue me; but in practice these sorts of matters will generally be resolved through the dispute process (assuming the consumer does not simply pay the wrongful charge out of intimidation), and in that process the property is always welcome to invest the resources and efforts necessary to fix the problem they created.

(Agree with your point re WoH account-related risks, of course, and I tried to make clear in my initial post that this approach is not risk-free, simply that some may consider the risks worthwhile in this circumstance.)