Your article concedes that whole grains contain anti-nutrients, but then concludes that if you are getting sufficient vitamins and minerals, it's not a major issue.
It could be, I guess. The human body is so complex, so I will not say that I know for a fact that these anti-nutrients are not causing major problems.
But you should at least keep track of how many foods with anti-nutrients you are consuming daily, and at some point realize that the math won't add up in your benefit.
One guy referenced a study in which whole wheat bread and beans were consumed with oysters and very little or none of the zinc from the oysters was absorbed. (but don't quote me on that ...)