On the other side of Greek historians was Dionysius of Halicarnassus, who was the first to suggest that the Etruscans were indigenous...mostly because (and not a bad reason either), they didn’t agree in language or customs with any people they were said to be related to in Anatolia.
Massimo Pallottino, the famed Etruscologist, has pointed out that whatever the origins of the Etruscan people, their civilization as we know it developed in Italy, and there I think he’s quite right.
Good point about the Etruscan vases with the Aeneas legend...it’s definitely a VERY old story in Italy.
Etruscan, on the other hand, was a non-Indo-European language, which had no surviving relatives in Asia Minor in the era of Dionysius of Halicarnassus, at least none that we know of. Its only close relative is the language which was spoken on Lemnos before the Greek conquest--how the Lemnian language was so similar to Etruscan is a difficult thing to explain for those who think Etruscan was indigenous to Italy. In Greek tradition the earlier inhabitants of Lemnos were "Pelasgians." Who the Pelasgians were is not clearly understood--there have been lots of theories, including that they were the same as the Philistines (who seem to have come from the Aegean before settling in historic Philistia).
Etruscan is not related to the other langauges of Italy. Usually when you have a situation like that (e.g. the case of Basque) it's because a language happened to survive in a mountainous or inaccessible area--but the Etruscan language is found in one of the most desirable areas of Italy, the kind of place an invading group might have conquered.
Italian scholars have tended to favor the theory that Etruscan was indigenous to Italy rather than brought in from the east.