It seems like the article is saying that as long as it is a mild case, and you are already somewhat fit, it is better if you exercise. However, if you are over 50, or moderate to severely ill, then don't. Which seems to make sense and it pretty common advice among gym goers.

Usually the saying is something like, "If it is above the neck you are better off exercising, below the neck wait and rest." Where above / below the neck refers to chest congestion versus nasal/sinus congestion.