I tend to pay attention to the author more than the web site. T-Nation has some good authors, some not so good and they tend to throw in nutrition recommendations into most articles. At any rate, in my opinion, Tony Gentilcore knows what he's talking about.
Core basically means everything from the hips to the ribs, in other words, the waist. You left the Erector Spinae out. ExList/WaistWt.html The main goal of core training is stability so the anti-movement type exercises are becoming more common.
It's not that I don't like bodyweight exercises, it's just that I think (of course correct me if I'm wrong) that unless you don't have any former training, they oppose too little resistance (unless it's something as advanced as a planche push up or one arm pullups, which however are also very technic and I am not able to do) compared to a weighted exercise (like suggesting push ups to somebody bench pressing loads) and thus I'd have to use 30 minutes just to X bodyweight exercise while I'd do 3 sets of a weighted exercise and be done with it in 15 minutes.
The point on the dead bug exercise was that it is often done wrong. I don't think it was intended to be the primary focus of core training. There were only 2 body weight exercises listed. The rest were all weighted. I don't know why you think this was about bodyweight exercises.
The 3 movements he recommended are: Anti-extension, anti-lateral flexion and anti-rotation. He left out anti-flexion because most already do deadlifts and squats which cover this off already. Do 1 exercise of 1 of these in each workout. That shouldn't even take 15 minutes. You obviously didn't read to the end of the article.
An older article, but still very good, gives different options for these same movements. free_online_article/most_recent/21st_century_core_training_1
I didn't want to overgeneralize, it was just what I found out most of the times by reading there, though it may be that I was unlucky enough to only read those "bang your head into a wall then lift until you puke" kind of articles.
I left out erector spinae because I thought it was trained as good as it could be by deadlifts.
I thought it was about bodyweight exercises because of those first videos, then didn't even consider the rest due to the "fancy" (for my standards, I forgot to add that I train at home with limited resources/space, just a barbell, plates and a crude rack), so I apologize if I wasn't as accurate as I should have been.
I'll read that other article as soon as I can.
Back to the exercises, shouldn't those ones I've listed cover that core purpose? After all, as isolated as one exercise could be, it involves more than just one specific muscle, and unless something isn't targeted I don't see a real reason to ditch them.
I'm slightly confused about this.