I'm not sure exactly why I've never thought of Greek yoghurt in the same way!
Why do you expect that? It can't be based on the name, since virtually all foods with an origin name were not actually made there. I'm pretty sure you don't expect Cheddar cheese to have come from Cheddar? Would you accept ordinary yoghurt that was imported from Greece being sold as "Greek Yoghurt"?
If I imported Camembert cheese from Cheddar, it would still be Camembert. If I imported Cheddar cheese from Hong Kong, it would be Cheddar. French toast sold at a Denny's in New Mexico was made in New Mexico, not France. Peking duck is duck prepared in a style characteristic of Peking, not any duck prepared in whatever style but sold in Peking. And Greek yoghurt is yoghurt prepared in a style characteristic of a Greek company that decided to sell thickened, sweetened yoghurt.
it might be a strange concept for non-europeans, but for us, this is one of the best things that came from EU integration. if I buy a copy, I want to know it's a copy and not original. simple as that.
This is not about protectionism for producers, rather the protection of consumers. Noone is telling the consumers what to buy, merely telling them what they can expect when they buy.
To take the example of wine, consumers of Bordeaux wines have accepted that since the classification of growths in 1855 there is a formalised structure and hierarchy of producers. One can know that wine from a First growth will be superior in quality to a lesser growth. From looking at the wine label, a customer immediately can tell that the wine will be of a certain quality without having to take a gamble. Codifying this into EU law allows no other winemaker within the EU to produce a wine with a label that claims the wine is a First Growth Bordeaux. This is great for consumers.
The EU is not protecting producers in that anyone can make wine to compete with these Bordeaux wines but cannot 'piggyback' off of the 'brand' (for want of a better word) that Bordeaux has built for its producers.
The reason for that regulation is a combination of protectionism on one side and a desire to be well informed about the products you're eating.