Customer was promised a call-back. Period.
Evaporating promises are a pet peeve of mine. If you say there will be a call back, there should be a call back. Period. I don't care how important you think you are, or how many fish you have to fry; you or your organization have made a promise. Take five minutes and deal with it.
If your subordinate has made that obligation without your approval, then the subordinate should be corrected, and instructed to call back and bring closure to the situation. If there won't be a call back, do not promise it. Putting a customer in no-mans-land between 2 managers is poor procedure, bad manners, and it's bad business. It's not as if the OP had been rude, demanding, or unreasonable. "Hotel doesn't owe him anything"? Wrong. Promises are obligations. All they had to do was call, reiterate their policy and ideally thank him for his former patronage while offering a simple explanation (we need to make sure all stations are available for our paying guests), and say that no payment was expected for prior charging. Closure. Promise kept. Simple.
Too many important things to do? I'll relate an anecdote about an important person.
An acquaintance was working as a sound technician and setting up for an event in a hotel. One of the speakers, as it turned out, was Henry Kissinger. At one point during the day this fellow and Kissinger ended up in the same elevator. During the elevator ride, and while walking down the hallway, Kissinger struck up a brief conversation.
3 years later, while working on a project in another hotel, who happens along but Henry Kissinger. He turns and notices this fellow working on some sound equipment.
Not only did Kissinger remember his name, but inquired about his wife, Mary, and their two children!
Not only did this illustrate a remarkable mind, but also a great person who took the time to connect with people despite being rather busy with important things.