The usage the author points out is odd, and one I would never use.
However, it is not brackets alone that is an issue.
The usage is strange!
Begin excerpt:
They may groan when Corky, denied the massive funding he’s asked for, tells the town council he’s going to “go home and bite [his] pillow,” the way I do now.
End excerpt.
The quote with brackets in it appears functionally equivalent to:
"go home and bite my [his] pillow."
I agree with the author here, and would add calling out the brackets alone is not enough.
There are well accepted and clear uses of brackets in quotes that are lumped in with this arguably, dubious construct.
I read the article title and thought, "Well, no. Is this some purist argument or other?"
Turns out it is not!
Standard bracket use is not in question. Not even mentioned. Normal bracket use does not change a quote at all, when done properly.
The bracket use the author is bringing to our attention DOES.
Go ahead, take a closer look at the full excerpt. Why did they do that?
About the only reason I can find for doing it appears to be a potential misunderstanding between "my pillow", as would be quoted, and the ending statement, "The way I do now."
Why?
The quotes clearly assign "my pillow" to Corky, as opposed to the writer, who post quote says, "I do now", but that is not good enough, apparently.
I would call this being too clear at others expense, as well as an insult to the reader, who is likely to wonder just why "[his]" got put in there.
Did Corky really tell the town council, "go home and bite pillow" broken English style? Of course not, so why bother with the use of a context or clarification device used to muddy both? Edit: Even worse is the case where Corky actually did speak broken English style, which is now rendered a matter of ambiguity because someone thought muddying up the language would help their prose be more clear!
Agree with author on this one.
That bracket abuse, and I am going to call it as I see it here, appears to be quite pretentious, while also adding nothing of value and considerable confusion!