[1] For varied definitions of "amazing", such as "conquer countries 10x your size", "invent 20 sports the entire world plays", etc.
I grew up in the UK but I've lived for 15 years all over the US, and it's always confused me that Americans are convinced that British food is bad. On a whole, British supermarkets have far better produce, in both quality and diversity. UK restaurants run the gamut from cutting edge fine dining and wonderful traditional food to home-grown variants of immigrant cuisine. It's a great place to eat.
My home town is legendary for Indian restaurants—to the extent that Birmingham-style Balti curries have made their way back to India. Before you claim that this is Indian food, not British, can you name an American dish that wasn't developed by immigrants?
Home cooking is far more popular in the UK than the US: anecdotally, most British people cook most meals at home, while few of my American friends know how to boil an egg and rely almost entirely on take-out. British celebrity chefs and cooking shows are famous worldwide. It's odd to claim that British food sucks while binge-watching our prime-time baking show!
I love America and a lot of things are better over here, but food—unfortunately for me—is not one of them.
I consider Tex-Mex as American and home grown. It also depends on your definition of "immigrants" since that path looks different everywhere (and across time). Texas was at one time Mexico (and even its own country plus a few others). But tortillas, beans, corn, cornbread are Native American. Many have simply lived here through generations and name changes.
I would also argue for BBQ[0]. I had to double check, but according to that wiki page it was from the Taíno who had inhabited Puerto Rico, which is part of America; which was acquired by Columbus, then brought to the mainland by the Spanish. Since Texas was a part of Spain for some time, there is a case to be made that the dish was not by immigrants if looked at from that angle.
[0] https://en.wikipedia.org/wiki/Barbecue_in_the_United_States
The difference with Tex-Mex is that its foundational items are Native American, so the distinction, imo, is that the main ingredients and how they are used is from America. Even though the Americas were populated by pacific islanders/Asians, no one would call Tex-Mex Asian food.
I don't know a lot about the making of Indian food, but I have not yet heard the argument that the base ingredients/spices and how they are used come from the British Isles. That's how I would "draw the line" in determining if it's British or Indian food.
That said, the best Indian food I have had was in London
So while I see your point, I wouldn't say a cuisine is always "from" the same place as its ingredients.