Bodybuilding is a form of resistance training. And there are multiple forms of bodybuilding, some healthy and some significantly less so. The above trainer seems to be talking about a sort of general fitness and casual bodybuilding that is indeed good for health and longevity.

Running is great, in moderation. But having reasonable amounts of muscle mass is also great. Most people are going to have better health outcomes looking like Brad Pitt in Fight Club rather than Andrew Norton