The big problem I found with this explanation was point 2, because apart from and, or, but, while and yet there are a whole bunch of conjunctions that introduce subordinate clauses (otherwise called conditional clauses), and subordinate clauses require a comma. Examples include because, as, since, and although. There are also a bunch of of conjunction like words that would normally require a semicolon if they were introducing a clause. Examples include however, thus, hence, nevertheless and therefore. Even this is not all that clear because these words can be preceded by a full stop if they begin a sentence or a comma if they form a minor interruption to a sentence.
I get the impression that on the whole it is best to use them sparingly. Some authors, like Patrick O'Brien, can sprinkle them about as they like, but you have to be a very good writer to get away with it. George Orwell disliked them and tried to avoid using them. Kurt Vonnegut loathed them. OTOH, it's better to use a semicolon than a comma splice IMO.