Despite the headine, the article is actually pretty sceptical about the quality of current machine-generated poetry, aside from some fluff about the "inevitability" of AI being able to write human-quality poetry. There's nowhere in the article that I could see which claims that "many people can't tell the difference." (Headlines are often written by editors rather than the writers themselves, and this one seems to have generated a particularly big disconnection between the two - I think the write has been hard done by here).

Besides which, often with these claims if you dig into them they start to fall apart. There's one about wine tasting that's often circulated - a study where people "couldn't tell the difference between red wine and white wine with added red food colouring". But IIRC the people in the study were first-year oenology (the study of wine) students, and I bet you (a) they'd be able to tell the difference between a Malbec and a Pouilly Fumé with red food colouring and (b) people who'd been tasting wine for longer (i.e. people who had more experience) would be able to tell the difference.

I'm reminded of a radio comedy panel game where the punchline to a joke was "bite the wax tadpole", and there was quite a bit of laughter around the fact that it was probably the first time in human civilisation that those four words had been used in that order before. AI may eventually be able to write something reasonable, but there's something very specific about good poetry ("good" is of course subjective) that I think is likely to always set it apart.