I don't actually like the stochastic parrot argument either to be fair.
I feel like the author is ignoring the various knobs (randomization factors may be a better term) applied to the models during inference that are tuned specifically to make the output more believable or appealing.
Turn the knobs too far and the output is unintelligible garbage. Don't then them far enough and the output feels very robotic or mathematical, its obvious that the output isn't human. The other risk of not turning the knobs far enough would be copyright infringement, but I don't know if that happens often in practice.
Claiming that LLMs aren't stochastic parrots without dealing with the fact that we forced randomization factors into the mix misses a huge potential argument that they are just cleverly disguised stochastic parrots.