I don't want to go too deep into an analysis of the study. Gelman's post and the accompanying discussion do a good job exploring the issue and it's too late in the evening to cover old ground. There are, however, a couple of points from the post and comments that are particularly pertinent:
1.Gelman -- "Each person is an individual, and I would not be surprised at all to learn that a treatment that is effective for most people can hurt others. Once you accept the idea of a varying treatment effect, it’s natural enough to think that the effect could be negative for some people."
2, There are other, not-so-mysterious ways that exercise could indirectly cause these adverse effects. Soreness and injuries can cause stress and interfere with sleep, carb-loading, sports drinks and energy snacks can be surprisingly unhealthy, and it's not unusual to hear someone excuse a big meal with the line "I worked out today."
The effect described in the article is both weakly supported and unsurprising but it's getting extensive coverage because it falls into one of journalism's most beloved genres, the it's-not-really-good/bad-for-you story, a type of article that allows reporters to pander to their readers and be counter-intuitive at the same time. If you can come up with a study which suggests that seat belts are dangerous or that bacon prevents colon cancer you will be swarmed with microphones.
Here's a an example we discussed earlier:
... (reported by the ever credulous NYT under the headline Bicycle Helmets Put You at Risk) was that of Ian Walker, a psychiatrist at the University of Bath. Walker, an opponent of helmet laws, put a sensor on his bike and rode with and without a helmet until he had been passed 2,500 times (see the curse of large numbers). To control for potential gender effects he sometimes donned a long wig (to get the full comic effect, check out Walker's picture below).Walker found vehicles came on average 3.35 inches closer when he was wearing a helmet (for context, the average passing clearance was over four feet).
If you carefully read all the way through Kolata's exercise article you can find all of the required caveats (New York Times writers are generally pretty good at cover-your-ass journalism), but even a thorough perusal could leave you with a wrong impression while those who skim the piece or simply read the first paragraph are almost certain to be mislead.
You might expect journalists to require a higher standard of proof for stories that might encourage dangerous or unhealthy behavior. Instead we get the exact opposite.