That case has one of the best explanations of where, roughly, you might expect a line to be drawn:
While every protected geographical indication may inevitably become distinctive of the reputation for particular style or quality which is associated with the relevant protected goods, it seems to this Panel that that is not the kind of โacquired distinctivenessโ which will of itself be enough to confer โtrademark or service markโ status for the purposes of paragraph 4(a)(i) of the Policy. As this Panel sees it, to hold otherwise would be to turn on its head the decision made by the framers of the Policy, that geographical indications as such would not be within the Policyโs scope. โChampagneโ may be among the worldโs most famous geographical indications, but that in itself is not enough for it to qualify as an unregistered โtrademark or service markโ under the Policy. For a geographical indication to be found to have acquired such status, something more than potential eligibility to succeed in a passing off action would be required. In particular, it would be necessary to show distinctiveness as an identifier of an individual trade source. On the record in this proceeding, the Panel is not persuaded that the Complainant has proved that kind of distinctiveness under the Policy. The Complainantโs claim that it possesses unregistered trademark rights in a โChampagneโ mark has therefore not been made out. There having been no evidence provided to the Panel of the Complainant possessing any relevant registered trademark or service mark, the Complainant has failed to make out its case under paragraph 4(a)(i) of the Policy.
Some of that is going to involve a look at market reality. For example, there is a lot of cheese made in the style of "feta" outside of Greece. In the US, I doubt consumers of feta cheese have any idea that it means more than a particular style of crumbly semi-soft cheese.