I don't know who's been telling you that, but no, that is false.
The main cause of headaches in caffeine withdrawal is believed to be the fact that caffeine affects the blood vessels in your brain, and that cutting out caffeine therefore changes blood flow, and your body takes a few days to readjust to that.
Water is irrelevant here. Which is easily demonstrated by the fact that caffeine withdrawal is the same whether you've been drinking large, hydrating American-style coffees, or tiny Italian espressos, or been taking caffeine pills without water at all.
The main cause of headaches in caffeine withdrawal is believed to be the fact that caffeine affects the blood vessels in your brain, and that cutting out caffeine therefore changes blood flow, and your body takes a few days to readjust to that.
Water is irrelevant here. Which is easily demonstrated by the fact that caffeine withdrawal is the same whether you've been drinking large, hydrating American-style coffees, or tiny Italian espressos, or been taking caffeine pills without water at all.