In a five star hotel, I ordered for a cup of coffee. When I was about to sip, I found a fly in the coffee. I complained. The manager apologized, took back the cup and brought another fresh hot one. But I realized that he bought the same coffee. I sued the hotel in a consumer court and won compensation. The question is not how I won the case. How could I recognize that the manager has bought the same coffee?
I don't expect the waiter to be stupid enough to bring a coffee already mixed with milk again. There might have been some color on the cup from your lips (assuming you are a woman) but again he should have seen that.
You could have told from the temperature which decreases when the cup is carried around. Maybe there was no steam in the air, no smell. But you said he brought a "fresh hot one" which confused me. I also thought about the surface of the coffee that changes from a gleaming one to a dull, black one after some time. Plus, the fly or the object that picked the fly could have had influence on that.
The manager came back too fast. In a five star hotel, one can expect good, fresh made coffee - and such coffee needs >= 5 minutes in preparation and letting it steep.
This is because good coffee loses too much flavour when not grinded literally just seconds before brewing.
So if the manager came back in under five minutes, he could not bring a new cup of coffee.
The fly was was a fly of a different sort...