This is true, but in political terms Tibet is just a small region of China (I am not drawing any profound comparisons between Tibet and Wales!)
I agree that there are distinct identities within England as well, I think any proud Yorkshireman would be equally offended if you told him there was no distinct Yorkshire culture. But there is this idea of Welsh nationhood which goes back a long way, and they do have their own language. But anyway, I'm not nationalistic and I think people of all cultures should be able to get long perfectly well.
As for the point made by others about Welsh teams playing in the English league, I don't really understand the problem with it?
They're there for historical reasons (there was no Welsh league, or indeed English league, when they joined a regional league which was eventually assimilated into an English league), and to be honest, the Welsh league is of a very poor standard; removing Cardiff and Swansea from the English league would be like taking well-supported teams in England and saying they could never progress beyond the conference south!