Precision in language (and identity)

You’re writing a story about people living in Toronto. Do you refer to them as
a. Torontonians
b. Ontarians
c. Canadians
d. North Americans
Every answer is technically right. However, there are different levels of accuracy within each term.
If people in Toronto are voting for a new mayor you’d probably say “Torontonians are going to the polls” rather than “North Americans are going to the polls”, because it more precisely communicates the identity of the people you’re talking about.
I bring this up in the context of a column written by Melanie Lefebvre and Alicia Elliott for the Walrus titled ‘We Didn’t Choose to Be Called Indigenous.’ ((Elliott has said she doesn’t feel the title accurately reflects the purpose of the piece.)) It’s a meditation on the way in which Indigenous/Aboriginal/Native/Indian people have been given generic monikers over the years, rather than being referred to by their specific nation.

“The continual refusal of Canada to acknowledge our names for ourselves, insisting instead on “Indian,” or later “Aboriginal,” or now “Indigenous,” has ideological roots in the same idea. We name you. We grant you your identity—or not. You are ours to name as we choose. “

By the end, they suggest some steps Canadians can take to take part in reconciliation, including, “Learn the treaty history of the lands that you live on. Learn how to say the names of the Indigenous nations who traditionally cared for those lands—in their language.”
In my read, it’s an ask to learn and think about Indigenous people not as a generic, catch-all category but in more specific ways: Dakelh are not Haida are not Annishnawbe any more than Albertans are Manitobans are Newfoundlanders or Canadians and Mexicans are Americans despite being part of North America. There is a certain amount of shared experience, but there are also unique historic and cultural characteristics that make more precise terms helpful.
However, in a somewhat less charitable reading, former Walrus editor Jon Kay summarized the piece this way:

In his subsequent replies, Kay makes clear it’s his belief Elliott and Lefebvre are arguing the word “Indigenous” is no longer an OK to use and are embarking in language policing:
“Ive read a LOT of pieces like this over last year. Lots of focus on labels. This one seems like a rhetorical ante-raise over the others.”
“In six months, there will be another preferred label. I’ll wait for that one.”
“the smallness is the problem. college students & social-justice activists think they’re saving the world by policing language on FB threads”
The thing is, I don’t understand where Kay’s reading of this piece comes from (I’ve asked him, he’s yet to reply).
One reason I don’t think Lefebvre and Elliott are attempting to prevent anyone from using the term “Indigenous” is because they use it themselves, multiple times in the piece.
They also specifically acknowledge the impracticality of referring to specific nations at all times, writing, “We could not be “The Hopitu-Oceti-Sakowin-Kanien’kehá:ka-Powhatan-Chahta-Annishnawbe-Beothuk,” and acknowledge there is some use in catch-all terms such as “Indigenous” to acknowledge shared/similar experience across groups as a result of the last 200 years or so.
The suggestion, as I read it, is simply to strive for the most accurate terminology possible when referring to Indigenous people: “Indigenous” works when referring to people from different nations, but if you’re speaking about an individual, find out which nation they belong to– how they self-identify– and use that.
It’s precision in language and it’s something I personally think is worth striving for.