There might be some sort of rules that govern when it is correct to use "the" and when it is wrong.

The rules may not necessarily be simple, however. In the worst-case scenario, they may simply consist of lists of cases where it is one way and cases where it is the other.

(As you no doubt realize, the same issue also comes up in German: why is it "Deutschland, Österreich, und die Schweiz" instead of "Deutschland, Österreich, und Schweiz" or "das Deutschland, das Österreich, und die Schweiz"?)

But ain't those rules fundamentally malleable by the perception of people and their adoption of those rules?

Yes, and the exact same thing could be said about any human signaling pattern, not just those that concern language. But don't make the mistake of thinking that this is a Fully General Counterargument against any claim about the meaning of a particular signaling pattern in a particular context at a particular time.

It isn't as if everything eventually becomes accepted. Language changes, but it doesn't descend into entropy: in the future, there will still be patterns that are "right" and others that are "wrong", even if these lists are different from what they are now. Not only will some things that are "wrong" now become "right" in the future, but the reverse will also happen: expressions that are "right" now will become "wrong" later.

An interesting example is the German word 'Pizza' (which happens to mean the same as the English word, i.e. the Neapolitan cuisine). People were endlessly arguing about how the correct plural form of 'Pizza' is 'Pizzen'. Yet many people continued to write 'Pizzas' instead. What happened a few years ago is that the Duden (the prescriptive source for the spelling of German) included 'Pizzas' as a secondary but correct plural form of the word 'Pizza'.

From what I understand, linguists actually consider "-s" the regular manner of plural formation in modern German, despite the fact that only a minority of words use it, because it is the default used for new words. (So the dispute you mention is perhaps really about how "new" the word "Pizza" is felt to be.)