It seems very hard for me to believe, because everything motivates them to do the opposite. Can you imagine the flood of people and businesses that would come down on a model that actually sounds like a human being? The ability to impersonate a person without any tells would be a dream come true for businesses, marketers and scammers alike. They could put in zero effort and get what looks like normal human behavior in return. That is just too tempting for any of the labs to pass up. Besides, all of them have picked profit over sanity 10 times out of 10, so the argument that they drew just this single line in the sand and none of them ever crossed it on purpose seems unconvincing, especially with the sheer number of models out there, corporate and open.
At least to me, the first Dall-E 3 images were more realistic in some respects than anything that has shipped since. Likewise, I don't think it's a coincidence that the conversational capabilities of today's frontier models aren't much better than they were a year or two ago, even though other aspects and capabilities have improved massively. If they wanted a Turing test-capable model with no superficial tells, they'd have it, so I have to assume they don't want it.
(Elsewhere in the thread someone else suggests that the conversational degradation/lack of improvement might be the result of increased training on synthetic data, and that's another theory that sounds reasonable to me. If so, it's another thing they could fix if they wanted to.)
We can safely say that the AI labs aren't deliberately holding back. There's too many different companies making their own models, and an LLM that doesn't feel like an LLM is too lucrative of an opportunity for one of them not to defect. They are obviously going all out with this and still can't get it. I think this is why OP's benchmark is so interesting, because it seems that there are a bunch of persistent LLM defects that can't be solved definitively. They can try to squeeze it by making these defects less likely, but actually resolving what's causing them probably requires a new breakthrough in the field.