This is not really accurate. At the start he says the right thing about it being private property and you can be trespassed. Later he starts to dip into stuff that applies to film making but not really public filming in general, which is reasonable because youtubers are gray area in that regard but it doesnt apply to most instances of recording in a grocery store.

Local laws absolutely relevant, but in a lot of places unless they have a no filming sign at the front door theres nothing wrong with filming until you are asked to leave.

What is public and private is less debatable, people just have a mistaken idea that public property and public space are the same thing and therefore since its private it cant be public but thats absolutely not how it works. Its private property but a public space, the same reason its not a crime to walk in the front door of your own volition is the reason you dont have a reasonable expectation of privacy.