I read the article and my take-away was that older cyclists/athletes should moderate their exercise, not stop it or cut back substantially. The examples it cited were older cyclists who were racing and training at very high stress levels. That is, riding at high intensity with greatly elevated heart rates and perhaps inadequate rest and recovery.

As someone else has already mentioned, the key is moderation and common sense. I am 61 and ride about 800 miles/month, about half of that from commuting, and my heart and general health are excellent. However, I have scaled the intensity of my riding as I've gotten older, and seldom participate in fast group rides any more. In addition to commuting, I regularly ride with several other guys in their 60s and we ride at a moderate pace. We stop for breaks more frequently than in the past and ease the intensity of rides in hot and humid weather. I've been doing a lot more bike touring in recent years, including some loaded tours, but not trying to set any speed records.

The article in Velo News is more of a caution for "Type A" personalities and competitive types who have a hard time moderating their exercise (or other activities).