Generally, any art that is not distinctly something else that was founded, codified and developed by people of a specific nation is classified as being of that nation in origin. The art in question may be a development of an art imported from elsewhere.
If I were to take my hapkido, karate, taekwondo, and kumdo and combine them into one art, found it, codify it, and develop it, then it would be classified as a US art, inspite of the obvious Korean and Japanese influences. This would be true even if I were to call it Dan-kwon-do, Daniel-kwan or use an entirely Korean term for the name.
That does not mean that I invented the techniques or that they were developed in the US. It only means that a US citizen in the US has put together a system based upon what he has learned.
Just as nobody calls taekwondo Japanese in spite of the influence of Shotokan. Nobody calls Tangsudo Japanese inspite of the even stronger influence of Shotokan.
Also, many arts simply are general arts with no national identity, but with national schools. All of Europe had fencing, but there are distinct schools: French school (which is what much of modern sport fencing is based upon), Italian school, and Spanish schools are all fencing and each is unique. Hungarian saber was also fencing and also distinct.
Likewise, people have wrestled since the dawn of time. Nobody claims to have invented wrestling. But different nations go about it in different ways. Frequently, there are different ways within nations.
Just my thoughts on the matter. Find what you like, train in it and be happy!
Daniel