How on EARTH can you say that with such certainty? I don't know what happened and neither does anyone else, but I will tell you one thing: if I were going to bet, I'd say that by the time the Italics got to far southern Italy I would say they were probably few in number and highly admixed.
Italy was heavily populated by the time the steppe people arrived. They just didn't have the same impact in Italy that they had in northern Europe. I mean look at the Parma Beakers or Sicily Beakers.
Of course, I'm speculating too, but I think with more knowledge of Italian pre-history, and at least I admit I'm speculating.
As for Otzi, I totally don't get your point. He was, indeed, a Chalcolithic person, that is, BEFORE the Bronze Age, and yet he already had, in the old parlance, "West Asian" ancestry, which hadn't made it to Spain. So, as I've said over and over again, that ancestry was entering from the east in a pincer movement alongside the steppe ancestry coming in across Northern Europe. Why you would assume that Steppe people would wipe it out in Italy and the Balkans the way they might have done in Central and Northern Europe, I have no idea. Goodness, northeastern and parts of Northern Europe were almost uninhabited and uninhabitable. Hunter Gatherers need a lot of land to survive. They had to keep their numbers low, no doubt through infanticide among other things. Even for the farmers it was extremely difficult; not until the invention of different kinds of plows in the Middle Age could the deep, compact soil of a lot of that area be farmed. That wasn't true in the south. Goodness, we have Thracians in the Iron Age who still had no steppe.