In short, half the test subjects in a four-week exercise program took 1000mg of Vitamin C (that is, one typical large vitamin C pill, though it's about 1200%-1700% of the daily RDA depending on which numbers one uses), and 400 IU of Vitamin E (again, one large supplement pill, 1333% of the daily RDA) per day. The results of comparing the two groups indicated that the "antioxidant supplements appear to cancel out many of the beneficial effects of exercise". In particular, it appears that the oxidants released in the bloodstream by exercise are a key part of the pathway by which exercise affects glucose uptake and insulin sensitivity, and dietary antioxidants block that pathway. This is particularly important with regards to type-II diabetes; those effects of exercise are important to preventing it and can in mild cases even reverse it if it occurs.
Moreover, the blog post references another paper in American Journal of Clinical Nutrition, which "showed that vitamin C supplementation seemed to decrease the development of endurance capacity during an exercise program."
As Derek says, "there's enough evidence to go ahead and say it: exercise and antioxidants work against each other. The whole take-antioxidants-for-better-health idea, which has been taking some hits in recent years, has just taken another big one."