As for your yogurt example, perhaps it's because it's less important to those of us who live really far from Greece. It might not even be desirable to have yogurt that was shipped halfway around the world!
Is it yogurt made from Greek people? Is it yogurt made by a Greek company located in Spain? Yogurt made from Greek dairy, outside of Greece? Yogurt made in Greece from Italian milk? Yogurt made in Greece from Greek milk, but in the Australian style? I can think of all kinds of reasons folks half a world away would care much more about what style the product is, than would care about where, precisely, it was produced.
Of course, when you're in a trade union with a country that has a vested interest in having a monopoly on a product, obviously they're going to be pushing semantics in order to come out on top.
For those of us not so close to Greece, having to call it Greek-style yogurt is just more word soup. (also, this happens all the time in the US; the 'Greek' would be written really large and then 'style' in much smaller letters)
OTOH, it's pretty clear-cut in the case of a product that claims to contain a natural ingredient, but have none of it, and not even have any semblance of the benefits of the actual product.
I'd argue this isn't true. Greek yogurt has distinct style and ingredients which, when I buy Greek yogurt, I expect in my yogurt. Anything else is not what I want to spend my money on. It's like feta cheese. Real feta cheese is made from sheep's milk and not cow. It's completely different if made from cow's milk (not the same taste nor texture).
"French wine" -> everyone would assume it was actually made in France
I don't know if there's a hard rule that anyone can come up with about this sort of thing.
(I always thought "Greek" was a style of yogurt.)
As a counterexample, these "Greek yogurt" [1], "Turkish yogurt" [2] and "Yogurt of Bulgaria" [3] are all definitely made in Finland.
[1] http://www.valio.fi/tuotteet/jogurtit/valio-kreikkalainen-jo...
[2] http://www.valio.fi/tuotteet/jogurtit/valio-turkkilainen-jog...
[3] http://www.valio.fi/tuotteet/jogurtit/valio-bulgarian-jogurt...
In short, we don't need laws limiting what you can call things, with regard to country of origin, as long as product labels clearly indicate the country of origin. I know full well the $1.00 Chobani "Greek yogurt" isn't actually made in Greece, but some Greek-named expensive yogurt at the fancy grocery store I can guess probably is, and then after checking the label a bit more closely and seeing "Product of Greece" or "Made in Greece", I know it is.
Now, if some lotion says "Aloe Vera Lotion", I expect it to be made with real aloe. I really shouldn't have to check the ingredients list (if it even has one; it's not a food so I'm not sure that's required).
It's common here(in the US) for "Greek yogurt" to mean Greek-style yogurt, and we would all ask "why!?" when confronted with that regulation. However, when you read stories like this - maybe that kind of regulation is needed. I've been buying aloe from walmart/target/etc for ages, and always assumed that the ingredient list wasn't a lie - now I realize that is not always true.
edit: typo
If a yogurt was labeled as "made in Greece" then it would be expected it came from Greece and would be pretty uniformly agreed as fraud / false advertising if it was learned the yogurt wasn't made in Greece.
Among other things it was one of the point of contention regarding CETA/TTIP.
What I am talking about is that every product in EU has to be what it says on the label - so Greek yoghurt has to be from Greece. French wine has to be from France. Apple juice has to contains apple juice, not just apple flavouring, etc etc.