Paco:
Why would anyone want to dive with a hangover?
I think that's a silly question. Someone would want to dive with a hangover because they want to dive, and look at the hangover as an unfortunate minor obstacle that they can deal with.
It's not like anyone ever said, "I've got a charter coming up in the morning, so I'm going to start pounding whiskey shots now to ensure I have a nice, head-splitting, hangover for the dive."
No one wants a hangover, but having one may not keep a person from wanting to dive. In fact, having made a few hungover dives in the past, I think the diving made the hangovers feel much better. When hungover, the prospect of weightlessness and a temporary escape from the ringing phones, honking horns, and other too-harsh noises of the surface world isn't totally without appeal.
I don't recommend the practice, but if a diver feels well enough to want to dive, and drinks plenty of hydrating fluids, I don't think it's the end of the world if they suit up and get in the water for a simple shallow-water recreational dive... especially on nitrox.
That said, I feel very differently about the matter if the dive is even a remotely challenging one. Anyone planning a deco or hard overhead dive, for example, ought to be at the top of their game, and shouldn't be drinking the night before.