The problem is that there are differing degrees of "Product of the USA" here. "Big Meat" wants to slap it on anything they want that vaguely touched the US at some point prior to packaging for marketing purposes. Absolutionists may want it to mean nowhere in the value chain that produced that particular animal does any other country appear, and may even say, yes, that means the car you mention is not made in the US. (Presumably there is a limit to how far back the analysis needs to go, since cows are not native to the US.) The guy on the street probably doesn't care, and may care about it for quality issues (perceived or real) or care about the vast majority of the profit of the value chain being retained in the US.
Generally, when it comes to product labeling in the US, the federal government declares what labels mean, and in the absence of that, labels have very little meaning [1]. In this case, the court majority ruled that the meaning the government outlines was fulfilled by the meat labeled as such in the package. This is not wrong, it just happens to not be the definition preferred by other people, and they're going to Congress to get it changed.
So, to answer your question, yes and no and maybe, all at the same time. Hence the problem.
[1]: It occurs to me as I type this that more of the labels could stand to be clear about which is which. If my bread says it is "whole wheat", is that in the set of meaningful, legally-defined labels, or is it just something the manufacturer felt like they could stick on because there was a whole wheat grain that accidentally got into the dough? I don't know, and my not knowing is the point, not the question itself.
The only loophole is short descriptions by default have an ambiguous meaning. “Made with Oak” could mean you used an oak spoon at some stage in the process. So, it needs to be extremely egregious which this case wasn’t.
(I'm using platinum ingot since that's how I'm assuming you'd buy a lump of platinum metal. If this is not correct, substitute for whatever the thing is you'd actually buy from somebody like Rio Tinto. I'd have used the platinum ore directly, but my understanding is that it generally is produced as a byproduct of other metal refining.)
If we can't include a copper heatsink because it was imported to the USA as raw copper ore... then can we even include foreign workers who come to the USA to work ? They may go home at any time... or they might be forced to go home... they might not even be authorized to work in the USA, or not let back into the USA (even if they were otherwise allowed to work) next season...
Again, we're arguing over where to draw the line, and that's why I dislike "Product of the USA" as a mechanism for meat labeling... everyone wants to draw the line somewhere differently, so it would be better to be more specific about labeling aspects of it, not the whole.
Copper can be sourced inside the US, if you didn’t then you have a foreign dependency in your supply chain which is something the DoD actually cares about for obvious reasons.
Any other definition is just meaningless marketing crap like “The Best” which is legally meaningless.
In my mind if a product has foreign decencies in it’s supply chain then it is not a product of the US alone. A reasonable exception for manufacturing equipment or IP owned by a foreign company.