For instance, chili peppers were introduced to asia by the portuguese during the 15th century, but now chili-heavy dishes are characteristic of much SE Asian and Indian cooking.
Is pasta characteristic of Italian cooking or do we need to look further back to ancient greek origins and say it's not really from there?
Are we sure we should credit either France or Belgium with the British 'chip'? While they argue over the origins of fries between themselves, and certainly their 'frites' pre-date the British chip-shop, they are cut very differently. Or do they both owe their heritage to Spanish "Patatas", as Spain had the potato first, and really, frying the damn things is pretty obvious when you think about it ...
Personally I think things cross-pollinate constantly, and very little can be considered solely and exclusively the property of one culture or other.
Pedant alert: Fish and Chips is not originally British! (It's only been a staple over here since the 1860s.)
The chips had their origin as Belgian frites, and the fish is from Sephardic Jewish immigrants from Holland, who picked up and modified the recipe for pescado frito. (Fried fish could be eaten cold the next day, so was suitable for shabbat.)
https://en.wikipedia.org/wiki/Fish_and_chips