Pain is your body saying "I'm injured. If you don't stop now, expect things to become worse, potentially causing permanent damage." No athlete I'm aware of pushes through pain unless they expect to retire immediately after, or go into surgery. Runners who do this tend to get knocked out of the sport. Good runners recognize pain for what it is and stop immediately.
Discomfort is different. This is what the article is talking about. Running through cramps. Throwing up but still not stopping. Feeling tired but still pushing ahead. Leg muscles sore but still holding pace.
Of course you need to be careful about discomfort too. It could be a sign that you're severely dehydrated, or have too few electrolytes in your body. This is mostly an issue for distances greater than a marathon, however.