I mean, the person you were talking to sounds annoying and incorrect in trying to claim some superior American cuisine over British cuisine, but they’re not wrong in listing foods that were originally from other countries as being part of their cuisine in a changed form.

Tomatoes didn’t exist in Italy until they were brought over from the Americas in the 1500s, and they didn’t become an established part of Italian cuisine until the late eighteenth century, but you’d be hard pressed to find someone who didn’t agree they’re part of Italian cuisine. And nowadays, there are foods in the US that are originally Italian but have clearly become new and distinct dishes, like Chicago deep dish pizza. So you’ve had recipes and ingredients passing back and forth across the Atlantic, and indeed throughout the whole world, for centuries.

I grew up in the UK but my mum is American, and she’s always made succotash, which is one of the recipes common in New England where she’s from. It was invented by Native Americans, and it’s been cooked by white Americans as well since the early 1700s. So, as long as Italians have been cooking with tomatoes. I live in Scotland and I’ve encountered plenty of American tourists claiming that their great-great-grandfather makes them somehow Scottish, and it’s definitely grating. But the fact is, there are many foods in the US that are either indigenous to North America or were brought there by immigrants and shaped over the centuries into something distinct and new, and that does very much form a cuisine, and a varied one.

Sometimes these foods are based on existing dishes, yes, but so is most food in the world. There are only so many basic cooking methods and a lot of cultures have their own version of ‘fried dough sachets filled with stuff’ or some noodle/pasta variant and so on. What matters is whether a dish is a distinct variant, such as how American-style barbecue is sweeter in flavour, uses different spices, and is smoked over wood whereas Mexican barbacoa is more savoury and traditionally braised in underground pits, and Jamaican jerk seasoning is more sour and spicy and a distinctly different flavour profile. Then there’s churrasco in Brazil, Korean BBQ, etc. There are a lot of different versions and elaborations on what at the end of the day is a pretty straightforward method of cooking meat. And some foods were just invented in the US, like New England clam chowder or Buffalo wings. The upstate New York town my mum grew up in is tiny, and yet there are a couple foods they eat there which you won’t find anywhere else, even in the rest of the state, because they’re local inventions.

Additionally, while opinions might differ as to whether British cuisine is good, per se, it definitely exists — if you’re interested, for example, Pen Vogler has written two social histories of British food which are really good:

https://www.theguardian.com/books/2023/nov/17/stuffed-by-pen-vogler-review-tasting-history

Or even to look at one specific foodstuff, A Cheesemonger’s History of the British Isles by Ned Palmer is one of my absolute favourite books, and it does what it says on the tin, tracing the history of British cheeses such as Stilton which have the same rich cultural history and pedigree as something lol Camembert. It’s fascinating stuff if you like cheese at all:

https://www.theguardian.com/books/2019/oct/23/cheesemonger-history-british-isles-ned-palmer-review