But why can't I call it Parmesan cheese?
Well, protected designation of origin (PDO) and protected geographical indication (PDI) are hugely important for producers. This is one area I'm familiar with it due to my family working in agriculture. Both PDO and PDI-branded goods are grown, raised and/or produced in controlled fashion according to clear quality standards. PDO and PDI certificates are not issued at random, but only to regions that happen to produce goods of particularly high quality or reputation.
A wine from La Rioja is much more than fermented grape juice from a particular region of Spain. It is made from an officially sanctioned variety of grapes in controlled quantities and aged at well defined ranges at a number of towns. It's a relatively complex and stringent regulatory system that allows for consistent quality assurance and reviewing. Nevertheless, La Rioja wineries have to fight with a number of foreign producers that claim to sell "Rioja wines", when in reality it's just terrible plonk that damages the brand and dilutes the value of authentic Rioja wines.
Even more outrageously, there's the case of unscrupulous Spanish, Italian and even Chinese pig farmers selling substandard cured hams as Jamón Ibérico, when actual Ibérico has a vastly superior taste, texture and aroma
owed to the breed of the pigs, a nutrition based on acorns and vigorous physical exercise, which makes for a ham unlike any other, with bright red meat and incredibly soft and thin layers of marbled fat that melt at room temperature. Those fake ibéricos come from industrial farms and they are not subject to the same veterinary inspections as proper ones, which is not a joke. We are talking about cured meats after all, which means that there's a health risk on top of a fraud.
Similarly, some people have been trying to pass terrible Eastern European truffles as Italian and Spanish black ones, when the difference in quality is staggering accounting to soil and climate.
Basically, PDO and PDI are much more than just a brand or a luxury halo. They ensure consistent quality and standards. As a matter of fact, producers from a PDO/PDI region that decide to break regulations will lose their certification and risk severe fines in accordance.
As for the Italian oil fraud, that's a different issue since it involves both the FDA and Italian authorities. The EU is relatively clear on this subject, but Italy has its own problems enforcing the law since they are dealing with activities closely related to the organised crime. I'm outraged at a personal level by the amount of thieving companies buying Spanish oil, bottling them in Italy (or even elsewhere!)
and then selling them at exorbitant prices in other countries as "premium Italian oil", which is a well known issue. Next time buy from an tested Italian brand or just buy some good Spanish one. One is not better than the other.