TBF, I think the lay media (as opposed to the priestly caste of technologist) is responsible for this. OpenAI and acolytes plaster disclaimers everywhere.
But it's been two months and as more instances of grievous falsehoods emerge, the gen pop should become more aware of the limits.
This isn't a Deep Learning thing, this kind of overhype to distrust to normalisation consistently happens as tech has loved faster than our ability to educate people about it.