Although I didn't read the article, from my personal experience, weightlifting during the week helps me focus, and in a way that cardio does not. In weeks in which I lift 2-3 days, at the moderate level that I do (say 45 min of using free weights and body weight lifts at a medium pace, nothing extreme), I'm much less fidgety than weeks where I'm not able to lift, but my brain is still sharp.

This is in contrast to biking or rowing at a moderate pace (pusing myself and getting pretty sweaty but not collapsing or wanting to barf) for an hour once or twice a week. If I do this, I am still less fidgety but I feel more mentally fatigued later on the day, and sometimes the morning after, I exercise. I attribute this to nutrition/glucose levels and hydration, but even drinking a ton of water and snacking won't fully ameliorate the issues. The same thing happens after a weekend of playing hard, like kayaking one day and hiking with my daughter in my backpack the next day. I'm often pretty unproductive on Monday (oh well... ;)

What works best for me is moderate weight lifting followed by like 30 min of moderate rowing or biking, twice during the work week. Although I might feel a bit more depleted after rowing than not, my overall energy level is higher than if I skip the cardio, and I recover more quickly from my weekend activities.