Well this might be a fabricated story or not, but really? you'd seriously ask your neighbours to immediately stop their BBQ with the family all sat out in the back garden, the garden table all laid with salad, snacks, condiments and all the other accoutrements that come with a BBQ with everyone sat around eagerly anticipating that first bite into their overcooked and charred cheap supermarket burger of the summer knowing it will probably the the only opportunity of the whole summer to have a BBQ given our crappy weather? What exactly would you have them to do? crawl back into their home with their tails between their legs, close the doors and windows to seal cooking smells inside and sit around the family table munching on their 'indoor BBQ' while looking out of the patio doors at the nice weather outside and the sight of your Y-fronts flapping in the breeze over the garden fence? On what level is this request reasonable?
Asking your neighbour to stop bashing the hammer constructing that garden shed at 10pm in the evening...that is a fair and reasonable response...but asking a neighbour to stop their BBQ on a nice summers day?...think that is overstepping any realistic sense of reasonableness. Sure anyone can make a request of anyone at any time whether it be a reasonable request or not. But that doesn't mean the request can't be denied for equally reasonable or unreasonable reasons, and the requestor has no right to be offended or angry at whatever response they get, as long as its polite of course.