Hormesis and the hygiene hypothesis suggest that "working out" can be good for the immune system too. Unfortunately variolation has become a difficult topic.
I don't think doing exercise trigger an inflammatory (immune) response although I might be wrong. Either way your point stand regarding its paradoxical effect on oxidative stress.
Exercise does trigger inflammation through a variety of mechanisms (eg.: increased tissue perfusion and diapedesis, oxidative stress, tissue damage...).
However it also releases endocannabinoids, which are anti-inflammatory, and causes a host of metabolic changes which are also anti-inflammatory.
The overall effect of exercise is to increase inflammation acutely, and to decrease it chronically. Regular physical exercise is overall more modulatory than inflammatory.
