If I read the article correctly, very strenuous exercise doesn't weaken the immune response, but rather, the body prioritizes the immune cells to certain organs following exercise. Presumably leaving other parts of the body less protected for a time. Moderate exercise evidently does not cause a significant immune system change.
Although I did find this part mildly amusing:
Q. Any additional advice for those of us who work out and wish to stay well?
Dr. Peake: Washing your hands often and avoiding contact with sick people will also help.
Ah, isn't that also why really sick, contagious people are placed in quarantine? And while I'd like to avoid contact with all sick people, they have a habit of not wanting to avoid contact with ME. You know, the people who go out into public places with a constant hacking cough or persistent sneezing, that sort of thing.
If sick people all wore signs around their necks reading "SICK PERSON" I might be able to follow that advice better. But I do wash my hands a lot throughout the day. Not over fears about germs, I'm no Howard Hughes obsessive in that regard. But rather because I hate the feel of having dirty hands, about which I am a bit hypersensitive.
Began during the days I played the piano a lot, and wanted to maintain my "touch". Playing with sticky fingers on the keys makes me want to retch. But the added bonus to my lifelong habit is that I've now learned it's also a healthy practice to follow. Good.