Beans and acids - another old wive's tale?
The claim that cooking dry beans in salted water results in tough beans has been thoroughly discredited. Now I noticed on Essential Pepin that he cooked unsoaked kidney beans in a liquid containing canned tomato. http://blogs.kqed.org/essentialpepin/...
The braise takes 2-2.5 hours, which doesn't seem to indicate a lot of extra time to cook the beans. Before I learned that acid and dry beans are a no-no, I made a vegetable soup in a tomatoey broth and my kidney beans never got fully cooked. Yet I can't imagine that M. Pepin would present a recipe that doesn't work.
Cooks Illustrated found that acid does slow down the cooking of beans, while making the water a bit alkaline (with baking soda) speeds it up. They recommend adding citrus juices and vinegar at the end of cooking. Tomatoes need some cooking time, so they recommend adding those part way through, after the softening has begun.
Hard water, with calcium ions, is more of a problem.
See their 'Science of Good Cooking' for more on this.