Starlight your neighbor is probably not growing any black tomatoes or other varieties that are more prone to Gray Mold like GWRs and a few other heirlooms. I had never even seen the stuff in 25 years of gardening and then I tried some black tomatoes. I loved them and planted more and more of them each year and found myself battling Gray Mold almost every season. It rarely spreads even to nearby plants unless they are black or it is really rainy and the plants are intertwined a lot. A very effective way to prevent Gray Mold most of the time is just to not grow the varieties that are prone to it.
Bill