It's not just the street runoff. You have to consider all the stuff in the water basin that is draining into the ocean closest to the beach. For example, many coastal communities might not have a sewer system, using septic tanks and leach fields instead. When it rains enough, some of the runoff gets into there (ever seen pictures of septic tanks improperly secured that pop out of the ground after a rain?) and then moves down to the ocean. Then you also have agricultural/animal runoff if there are farms or ranches in the basin, and potentially industrial runoff if there's any heavy industry in the area too. And even if you have none of these factors, just the simple influx of nutrients can cause things like algal blooms that can be just as bad.