Not quite, as the geographical indication not only only means that it was produced there, but also has other constraints on how it is produced, etc... So it is

Not quite, as the geographical indication not only only means that it was produced there, but also has other constraints on how it is produced, etc... So it is very much a brand, in the very same meaning, that it doesn't necessarily guarantee quality, but that the brand of the region is a means of ensuring some quality standards. E.g. there are wines from certain regions, but they do not have the geographic indication, as they have not been produced according to the regional standards. And going with food it is even more important so, as it is close to impossible to reproduce the climate and terroir somewhere half around the world. That doesn't mean, that it is worse, just that it is not the same. Take Lambrusco as an example, they do have (or had?) a bad reputation and suffer for it. It's a good motivation for regional producers to keep each others in check.