This sounds like a "Well, we've got the grant money...better come up with something." If you do nothing but sit around all day and stuff yourself with antioxidant vitamin supplements, then yes it will have an adverse effect at some point. They should be taken in doses to match the stress your exposed to.
This is no different than saying don't drink to much water. It can be bad for you. That's true in the total extreme where death can occur. But somewhere between dehydration and drowning there is a lot of room for error. The same goes for antioxidants.
The article is somewhat interesting(you may be right about somebody just making noise) in that they are talking about eating too many high antioxidant "foods" rather than supplements. One of the reasons that some of the studies using antioxidant supplements have turned out not show value has been thought due to our still uncertain knowledge of how our metabolism deals with "fractions" of whole foods. The interaction of different components of food may have a cascade/sharing effect that may be eliminated by taking just a part of a food substance.