As I guy who was at the Rifleman Challenge, where this vid was shot, and a guy who just went through the Citizen Close Combat course, I can give you my opinion of this subject. In the vid, we were just given an intro to room clearing techniques, on the 3d day of training. We were pretty smoked and did some things incorrectly. These were subsequently corrected. When I got to C3 class, I again saw what we did wrong, and spent a couple of days learning how to do it correctly. To answer the criticism, the corners are (usually) cleared before entry, using this technique. It is just unfortunate that the vid picked up our mistake. I'm sure you can cherry-pick anything you like and find mistakes in it. That does not invalidate the training program, as far as I'm concerned.
Let me explain where this came from. The instructor deployed to Iraq, using all the techniques he had been taught by "DOD". The vaunted COI so loved by .gov types. Well, he found out that a lot of it was bullshit. In fact, a lot of guys got killed before they figured that out. Here's an example. The team is stacked and ready to enter a room. Uh rah, let's jump on in there and kick some ass. They flood the room, and try to go for domination. In the meantime, the oppo has cut a little mouse hole to the adjoining room, and have a guy with an AK sitting in there. As soon as the guys flood the room, he opens up, through the opening, and just massacres the entry team. They try to return fire, but the aperture is so small they can't get any hits.
What this led to was using a double "pie" technique, from the doorway, which allows you to scan (and service targets) on about 85% of the room. This way, you're not committed before clearing a good portion of the room. If you did hit a prepared position like this example, you could more easily pull back out of the way. Then before entry, you both "pop" and clear the last 15% of the corners you couldn't see. Again, you're not in the room yet. You "roll" in, check for targets, then enter. Once you enter, you run the walls, to your domination point.
Again, when done correctly, this is a very viable technique, in my opinion.
So if you want to blame someone, blame the dumb-ass students who didn't do the entry correctly. The COI is GTG, in my opinion.