I think that customers who are rude and behave in an entitled way are very disappointing. Threatening to leave poor reviews over ridiculous things, so holding shop owners to ransom, is really poor behaviour.
However, there is a difference between such behaviour and a customer making a request for something that the owner wouldn't openly advocate, but can easily meet. I maintain that those in customer-facing roles need to be prepared to graciously accept a certain level of customer absurdity and accept it with a smile - people are strange, it is just a fact. Arguing with every customer who makes a slightly unusual request, pulling faces or gossiping with the other staff about them or past customers is all poor form. It sends out the message that the customer doesn't matter. Service with a smile is the thing wherever possible.
And yes there will be times where customers really are taking the piss and the owner will have to be firm but polite in saying no to a ridiculous and unreasonable request - still with a smile if possible.
However, asking for an extra empty cup, is not in this bracket. The owner should have just smiled nicely and handed over the cup and said 'enjoy your cream tea' - nothing was gained by not doing this, in this circumstance.
Instead,the owner clearly felt all indignant and self righteous and determined to assert HIS rights as the owner. Of course he was able to do that and did do so, but it makes me wonder how good any of his customer service is if he reacts like that to such a minor request - doesn't sound like a great cafe.
A lot of these things are not about 'rights' and those in customer facing roles know that in the long run, accepting the public do strange things and behave oddly, with a smile, is in all but the most extreme cases the best way to proceed.
Think of the best cafes and restaurants you know - you might not consider asking for a second cup in any of them, but if someone did, imagine their response. In the best customer service places, even the oddest request will be met with a warm smile and the customer allowed to leave feeling well-served, even if inwardly the server considers them a twat!