There's a difference between soreness and pain. My muscles get sore all the time from exercise, but it's not painful. That soreness just tells me I'm probably going to be a little bit stronger because of the exercise I just did. (Of course it's a continuum: certain higher levels of soreness mean I probably overdid it.)

Joint pain is a whole other thing, though. Usually joint pain means that you're doing some sort of exercise incorrectly, or that you're using too much weight or intensity for your current level of physical fitness. Or you have a previous injury that can't fully heal and there are some exercises that you just shouldn't be doing, but you do them anyway.

But I think the author is talking about less pain in a different way. For example, I threw out my lower back 25 years ago in college, and it's never been the same since. But doing core exercises and strengthening the muscles around that area means much less chance of pain doing regular day-to-day activities.