If someone says “I’m allergic to coffee but would love a glass of water” that’s a clear no to further offers of coffee.
It's a clear no to coffee, but not to associated offers intended to 'take the mean look off' a visitor sitting with a glass of water 'What about tea? Are you sure? Or I've hot chocolate? Cocoa? Ovaltine? What about this cappuccino in a sachet are you sure you're definitely allergic to that, too? Water looks fierce mean -- what about a Coke? Fanta? Orange juice? A smoothie? Or, if you really won't have anything but water, what about something with it? A biscuit? Some fruitcake? A scone? A yoghurt? A bar of chocolate? A sandwich?'
This is my mother, and my aunt, both born in rural Ireland in the 40s, but longterm city-dwellers.
And if you, say, eventually wearily agreed to a scone, you would be presented with a plate with at least two giant scones, already covered in jam and cream, because 'one looks mean'.
My mother also has form for offering things she thinks the visitor might expect but which she doesn't actually have in the house, and disappearing into the kitchen to either knock up a batch of scones from scratch and/or sending a child to the shop to buy some approximation of whatever it is she's offered some unsuspecting visitor. Who probably only wanted a glass of water... 
In Ireland you refuse twice and accept on the third offering
My mother would regard this as incredibly precipitate, the equivalent of someone literally snatching something out of the hand of the offerer. 
It is absolutely exhausting to be around. And we have never been able to train her out of it. I have been telling my mother for a good thirty years that I prefer a cup of tea by itself I don't like it with food but she still thinks it 'looks mean' and can't prevent herself from trying to press food I do not want on me.