The complaint isn't about the particular other order, but the fact that the order is ambiguous. In this case that doesn't matter, but often it does.
Americans memorize inches and yards, and often also memorize centimeters and meters, and working with either is fine, but we're not so often faced with numbers where it might be inches or centimeters and we have to figure out which (and when we are, it's sometimes a pain - certainly a bigger pain that working with known units).
Or, working with your language analogy, please go fetch me some "pasta" without knowing whether I'm speaking Italian or Polish.
… all the major predominantly English speaking counties will use mostly hyphens in the dd-mm-yyyy format. So although there is ambiguity, it’s easily resolved by picking that as the default mentally and only back tracking on failure.
Now in the more general case, this whole thing feels like a lieutenant/leftenant situation. We are annoyed simply because it’s not they way that we do things in a peculiar case, when otherwise the language is fully intelligible.
Even people in non-English-speaking countries write in English all the time, especially on the Internet.
Picking one default and back-tracking on failure really isn't that comforting nor the constant reminder that the date you thought it was might be something else.
Since the text itself doesn't clarify, context is the only way of resolving any of the scenarios. In each case it's usually sufficient and often not all that hard. But it's always harder than if the system in use was made explicit, and I understand the complaint (even if my annoyance at the ambiguity is quite significantly below the level where I would have complained myself, particularly in this case).
Americans memorize inches and yards, and often also memorize centimeters and meters, and working with either is fine, but we're not so often faced with numbers where it might be inches or centimeters and we have to figure out which (and when we are, it's sometimes a pain - certainly a bigger pain that working with known units).
Or, working with your language analogy, please go fetch me some "pasta" without knowing whether I'm speaking Italian or Polish.