Yes he is entirely wrong.
When the gun is broken and empty, it cannot be pointed. The stock and action are pointing in one direction and the barrels in another. It is in one of those rare conditions where it is totally safe.
Short of carrying the stock in one hand and the barrel in the other you really can’t make a gun any safer.
I used to carry my old single shot .410 broken over the shoulder like that or at my side in one hand.
That's true, of course. But, I think the point where the guy is technically correct (and, again, it's a technicality--the gun was safe, and the guy is clearly trying to get attention for his new site) is that every gun--even in the rare conditions where it is totally safe--should be treated as if it is not totally safe. The reasoning behind that is that people are creatures of habit, and so you want people to be in the habit of carrying the gun in the same way (muzzle down), regardless of whether the gun is loaded or broken and empty.