I mean that's somewhat his point (if I understand him correctly). All intelligence could effectively be described as a "stochastic parrot" as a result, calling something a "stochastic parrot" is a roughly meaningless insult that is really a thinly-veiled way of saying "no it's dumber than me" without actually using those words.
And his point is, it's essentially a defense mechanism in people when challenged by something that is much smarter than expected to overly emphasis it's mistakes and fall back to "no it'd dumber than me" than evaluate it for what it actually is.
I think that's the issue. It's a defense mechanism.
If you replace "stochastic parrot" in most of those comments with "it's dumber than me" you see what the comment essentially is. "It's dumber than me. I'm smarter than it, I don't need to be worried about it".