The credit company didn't receive a signed authorization from them to hand over the money to the hotel, so how could this possibly have happened?
The actual credit card number is *the* authorisation to charge the card; the money is only "handed over" 2-3 moths later when the customer has verified the bill and agreed to the charges by him/her paying the credit card provider.
The "signed authorisation" is another thing: It is a piece of paper with the card number, the name of the card holder and card holder's signature. This authorises continued charging of the card and is quite hard to get out of. The best way is a certified letter, complaint letter to credit-card company, then report the card stolen so it gets cancelled for sure.
The system is somewhat flawed that, in the interest of expediency & convenience, the card number is "enough", but, the credit card providers are not handing out any money of their own and they are quite draconian in dealing with abuse: "Too much" trouble with a business and the credit card facility is withdrawn, there is A.F.I.K. no restoration procedure and the blacklist is shared with the other card providers, so, that business is fucked, basically.
So, in this case, sure, they can go right ahead and charge 100 quid to the card, but, they only get this money after 2-3 months, when the customer has paid the bill! The customer complained, they will not get any money at all until the dispute is resolved.
The first step by the card provider will be to request the vendors proof of customer authorisation for the charge (signature on card receipt or the pin code entry). If the vendor does not have this, it have to prove that the charge was normal practice & justified - raiding of the minibar & nicking the towels would do it - random charge for complaining on internet site ... probably not. If I was that business, I would claim that "it was a mistake by staff" and revert the charge immediately. Maybe nothing more will come off it then.
They sound like real idiots at that place. Or maybe they are just grabbing whatever they can on the way out!