> That's the thing, she wasn't Queen of England in the same way Trump isn't President of Texas.The same way in that both are true, but not really the same way beyond that. Texas is separate-but-subordinate sovereignty from the United States, England is not a separate sovereignty from the United Kingdom, it is one of several older sovereignties that was fused to form the UK. To the extent that laws still in force in the country of England refer to the monarch of that kingdom, those references now apply to the monarch of the United Kingdom.
> The Treaty of Waitangi might use that term, but it is simply incorrect, even if they are well educated.
The interesting thing is that the Treaty uses the correct formal title in the introduction, but then uses "the Queen of England" in the individual operative articles. Honestly, looking at other treaties of the Victorian era that are similar in context (dealing with entities that are ceding authority and becoming subject, as distinct from treaties with entities that will continue as independent sovereignties -- there is a pretty big stylistic difference here, if you compare, say, the Treaty of Waitangi or the Stone Fort Treaty with the treaty with the Republic of Texas addressing the African Slave Trade), it looks like possibly a quirk of the drafting of the particular text, using the shorter outdated title where more typically treaties would just use "Her Majesty the Queen" in the interior. OTOH, this is also earlier than the other comparable treaties I can readily find (like the treaties of the 1870s with various Canadian First Nations), so the style may also have shited over time; in either case, the interior references are clearly less-formal references with the formal and correct title at the beginning.
The opening of the Treaty of Waitangi is: "HER MAJESTY VICTORIA Queen of the United Kingdom of Great Britain and Ireland regarding with Her Royal Favor the Native Chiefs and Tribes of New Zealand and anxious to protect their just Rights and Property and to secure to them the enjoyment of Peace and Good Order has deemed it necessary [...]"