Maybe you misunderstood OP's point and the English language can be confusing. It's south-the region, not south-the direction. "South of the Americas" means "the south region of the Americas" which is not "south of where the Americas end". Or like the top of your head is the upper part of your head, not your hat.
Everyone knows Venezuela is in South America. Which is not south of where the Americas are (Antarctica) or, confusingly if you're US-centric, is not in the American South either (Texas).
The problem raised above and the root of the confusion is that the US adopted "America" as their own instead of what it actually is, the name of 2 entire continents, the Americas. American South means US South just for US-centric commenters.
To the world this is like Germany naming itself Europe and then claiming Bavaria is European South, different from Southern Europe (e.g. Greece) or South of Europe (e.g. Greece of Africa, depending on how you spell or understand this expression).
I understood the point about the American South just fine.
I then supplied an analogy about the South of England, which I reckon to be closer to home for someone who made the distinction about the other side of the Atlantic.
That South of England analogy, by the way, was a description that I didn't know of myself until I went looking for something like that while drafting the previous response.
(After that even my smooth, featureless American corn-fed brain became willing to accept London as being somewhere in there.
Even though I know quite well that South of Cincinnati is not Cincinnati, but is instead Kentucky.)
That analogy would work better if England and France weren't very different places with very different names that nobody ever really confuses, except if you stumble on that quirk of unclear language (direction from the center, or direction from the edge). America and America are different places with the same name, which is not actually the same name because one of them is "U.S. of America".
Australia might be a better analogy/confusion. The continent also includes New Zealand and the country officially called Commonwealth of Australia is commonly referred to as Australia. At least in this case nobody considers New Zealanders to be Australians based on the continent name, or at least I could not find anything about this naming ever being used. In the Americas both continents are "America" and all people are "Americans", like all people in Europe are Europeans.
Any countries where a city (the capital) is named exactly the same will also check the confusion box.
It's fine that you're confused, I guess. Or at least: I am certainly willing to accept that I am powerless to impart any top-down disambiguation of any descriptive expressions. I can't do anything about there being a plurality of Americas in the world. It is possible that there will also always be football, and football, and that the two sports will always share the same name despite their clear differences.
Everyone knows Venezuela is in South America. Which is not south of where the Americas are (Antarctica) or, confusingly if you're US-centric, is not in the American South either (Texas).
The problem raised above and the root of the confusion is that the US adopted "America" as their own instead of what it actually is, the name of 2 entire continents, the Americas. American South means US South just for US-centric commenters.
To the world this is like Germany naming itself Europe and then claiming Bavaria is European South, different from Southern Europe (e.g. Greece) or South of Europe (e.g. Greece of Africa, depending on how you spell or understand this expression).