From Ali Arikan, Istanbul, Turkey:
You ask if there isn't any evidence in the comics that The Hulk and Spider-Man exist in the same universe. The answer is yes. The two have met on quite a few occasions, have fought each other in their many different incarnations (Green Hulk, Grey Hulk, Intelligent Green Hulk, Black Costume Spider-Man, Symbiotic costume Spider-Man, Clone Spider-Man, etc), and not necessarily only in NYC. In fact, the Hulk doesn't necessarily live in NYC: in many of his guises, Bruce Banner, his alter-ego, is always on the run, as was the case in the TV show, and the most recent film.
Marvel superheroes meet each other rather frequently – and not just in annual crossovers across the board. Spider-Man and the Fantastic Four, for example, guest in each other's titles quite often. In fact, it is very difficult to imagine an NYC with Spider-Man, that doesn't also make reference to the FF. Of course, the two properties are owned by Sony and Fox respectively and there has not been any kind of crossover in any of the five films.
The above two paragraphs remind me of a scene from a Halloween special of The Simpsons. The zaftig comic book guy is walking down the street, reading a comic, as he exclaims: "But Aquaman, you can't marry a girl with no gills. You're from two different worlds." He raises his head, sees a nuclear bomb rushing straight at him, and the realisation dawns: "I've wasted my life."