Yes, I agree, sport can improve someone's general health, but not everyone's. Some people, usually older, if not already exercising, or hasn't recently, may experience heart palpitations, or using Arthrofibrosis as an example, sometimes exercising can do more harm than good. Exercising while eating unhealthy foods will be most utterly pointless, and possibly cause hormonal complications or differences later on. As exercising can be healthy for you, it can also be somewhat dangerous if you believe you are overworking your system. If you want to exercise, however, make sure you are in a well-ventilated room and have plenty of water.
I agree that doing workouts while not following healthy nutrition doesn't make any sense at all. However, elderly people still can improve their health, they just shouldn't begin with hard exercises. They had better do light gymnastics or yoga, gradually increasing the strain in order not to get any injuries. The same scheme works for other people, for example, for those who have some medical contradictions. The only thing which they should do is to find the right type of sport for them. Ordinary people, who don' t want to overwork their organism, should consult with a trainer or find information in the Internet in order to determine the time and the frequency of their workouts.