Also, for meat, origin labelling is mandatory, but you usually see all three: "raised in", "butchered in", packaged in". If I understand the case in the article correctly, they're saying that if any of those three countries is the US, you can slap a "Product of the USA" on it and be done with it, which just wouldn't fly in the EU.
To be honest, these protected denominations favour the producers more than the consumer. If you think about it, from the consumer's perspective, it doesn't really make sense to prevent somebody in Florence from producing Prosecco, if they follow the correct procedures and use the correct grapes. The same applies for meat origin labelling, why should I care if my steak comes from the UK? I would understand Argentina... I find way more relevant knowing the breed rather than the country of origin (What's this? Angus? Chianina? https://www.sainsburys.co.uk/gol-ui/product/steak/sainsburys...)
But I digress.
I’m not an expert, but roughly speaking PDO (https://en.m.wikipedia.org/wiki/Protected_designation_of_ori...) means that the entire process follows certain procedures, ingredients come from a particular area and production happens in certain areas (usually the same as the ingredients).
PGI (https://en.m.wikipedia.org/wiki/Protected_Geographical_Indic...) instead is looser.
For instance you may have PGI Tuscan oil that is produced with North African olives, while Lametia DOP (a PDO oil) must be produced near Lametia Terme and must use Carolea olives from the same area.
You can’t label your oil “Lametia DOP”, if you produce it near Milan or if you use different olives.
All this to say that for “product of USA” to make sense, it should not necessarily mean that in order to get that label all ingredients must come from the USA. You probably miss a PDO-like certification.