Yes, but it decreases in the Copper Age, so I don't know how much would have survived in Northern/Central Italy. (I don't recall them saying it was all from the Neolithic, but maybe I missed it somehow. I'll go back over the paper.) It might be different in Southern Italy, of course, which is why, as you know so well, we so desperately need Bronze and Iron Age samples from there.
Then, the levels increase in Southern Italy, so I doubt the Neolithic could be responsible for it all. The question is, when did it arrive, yes? Did some arrive in the Copper Age, in the Bronze Age, in the Iron Age, In the days of the Republic and Empire, all, or just some, and what was the ydna like at each time? I can't imagine that there wasn't a boost at least in the Iron Age from Greek migration. Modern mainland Greeks may be slightly different, but ancient Greeks must have been pretty Mycenaean like going by the Empuries sample.
What we do know is that the Hellenthal group and the usual suspects were completely wrong about it arriving during the Post Imperial Age with some supposed mass migration from Byzantine areas.
Amazing, isn't it, how not only the amateurs, but even some of the scholars who buy into cliches have gotten it wrong?
Btw, if you join the magazine, which is free, you get access to certain papers without having to pay for them. It took me a long while to figure it out.
As to your post 443, that will be the second or third time that material was quoted to them. I guess if they don't want to acknowledge what it says in black and white, they just won't. Maybe I'm wrong that combatting nonsense with facts works.