Is the basic loading of a firearm; not under stress, time or pressure. One performs an 'administrative' reload in two circumstances; either when preparing for the daily carry (if one does an 'administrative unload when ceasing daily activity) OR when ordered to load on a cold range. The technique of loading from a magazine with only one loaded round comes from IPSC, IDPA or other 'action' matches. In defensive carry, I can see no reason for any magazine intentionally loaded with one round (other than possibly when loading up for the day, prior to need.)
The administrative reload is a valid exercise, albeit limited in scope. Done correctly, the process prepares one for action and limits the hazards of manipulating the firearm. (Like putting a round through the bedroom wall, for instance.)
The video maker has a point: if the pistol and magazine work properly, the first round in the magazine should indeed chamber when the slide is racked. However, in an administrative reload, a press check should not be considered improper. I find it somewhat comforting, if nothing else. However, once loaded, there is no need to check the sidearm again (and again and again and again).
Once involved in a lethal confrontation, a press check is immaterial. Once rounds are fired AND one comes to a lull in the immediate activity, one RELOADS fully, either by a fast magazine change or full revolver reload. There is no point in 'checking' to see how many rounds are left in the sidearm to be fired. (I will abstain from the discussion of 'retention' at this point. One does what the circumstances require.)
I further find the practice of shooting a semi-automatic pistol completely empty - slide lock - prior to reloading to be counter productive. A commonly reported phenomenon is shooters in a defensive encounter typically fire more rounds than thought. So if the immediate threat is handled, RELOAD, don't count.
(Old bullseye shooters can typically count to five without conscious effort; old revolver shooters can typically count to six. It is an acquired skill and in my case, done without intention to 'learn' the skill.)
One of my dictums for defensive use is the best place for ammunition is IN the sidearm (or long gun, for that matter.) Keep the gun full.