CH,
I will try to answer to some of your statements/questions, though I have a feeling this will not convince you even a bit (but well, it wouldn't be me, if I hadn't try):
I didn’t find where it mentions “surface within considered area”, only the entire surface.
Illustration doesn’t show it on “per unit basis” either.
Y14.5-1 is no different.
You could not find it because it is simply not there. How can "extension of principles" be defined in the standard? If it was there, it would not be "extension of principles" but a rule.
About being “rather worried if the local area was convex”, I may assure you that your “plate” will rock anyway on either convex or concave surface, because there is no guarantee that surface will always match all 4 corners of your 1 x 1 area. So why not to extend principle even further and specify 1 x 1 x 1 triangular zone?
The surface does not have to match the corners. The surface has to rest on at least 3 high points. And it will always rest on at least 3 points - the problem is that those points may not always be the high ones. As for convex surfaces, it is interesting that both sources - the standard (para. 6.5) and the Tec-Ease's tip - make remarks that for this type of surface tangent plane concept has to be treated with some kind of caution.
To me Parallelism per unit makes as much sense as applying Tangent requirement to Flatness. Could that be considered “extension of principle”?
No, it couldn't. Tangent plane, by definition, is perfectly flat, so Flatness requirement would be useless, illogical, illegal or whatever you want to call it.
I also liked how you changed your argument from “from purely geometrical point of view there is a difference” to “Again, forget about math”. Well, whatever helps you thru the night.
Flatness or Flatness per unit tolerance zone is not tied in rotation to anything. Parallelism or Parallelism per unit tolerance zone is always parallel to datum plane. This is why I said that from purely geometrical point of view there was a difference. And I stick to it. If you do not like the wording, change it to "Y14.5's point of view" or "my point of view". I do not care. The clue was: "THERE IS A DIFFERENCE". No offence, but in my opinion you are simply nitpicking on a single word which isn't really crucial for the meaning of my response. You are just attempting to make it important for the purpose of proving that I am wrong or inconsequential. (Or maybe for the purpose of hiding that you are incapable to admit you are wrong in this case :-])