Isn't the "good for your mouth" argument that saliva is sort of nature's mouthwash, and sugar free gum encourages our salivary glands to keep working, which after eating helps keep stuff from doing our teeth in?
Brushing's better, but I don't know many people that keep a travel toothbrush and toothpaste with them when they go out to eat, much less brushing after every meal at home.