Because no one calls where they live a nation? Country is the generic people term for place you live, we don't care about the legal distinctions and specifications.
It's less of a legal distinction and more of a definition thing. He is objectively using the wrong word.
It would not be incorrect to refer to the people of Puerto Ricans as a nation by the definition of the word. The word nation does not refer to a place but a group of people.
Kurdistan doesn't really have a central government like that, nor fixed or well defined borders. Keep in mind that the concept of a "Nation State" is really only a couple hundred years old.
If that counterexample doesn't satisfy you, then Somalia should. It is a country without a functioning government, which has two nations inside of them of the northern and southern Somalians which are completely different, and neither of which have any sort of unifying government.
The “people” and the “territory” are not the same thing, but both words “country” and “nation” are used more or less interchangeably to apply to either.