You hear this on a regular basis, often from Texans. The fact is that many delicious traditional (and non-traditional) chilis are made with beans and/or tomatoes. There is in fact some basis for this myth. Traditional Texas-style chili is made with meat but without beans or tomatoes, and it can be great, but that’s just one regional variant.
What about “Cincinnati” chili? I used to think it was meant as a variant on southwestern chili, and a very poor one at that. I since learned that Cincinnati chili is actually a dish invented by Greek immigrants in Cincinnati and meant as a spaghetti sauce or hot dog topping. It has some chili powder in it, but the main flavor comes from traditional Mediterranean spices such as cinnamon, nutmeg, cloves, and cinnamon. Learn more about Cincinnati Chili here.