There have been a few papers on the topic of Etruscan origins that argue in favor or against the Anatolian origin hypothesis. Two main lines of evidence exist on the topic: discontinuity between Etruscans and modern Tuscans (except some isolates); (perceived) similarity between Etrsucans' mtDNA and that of modern-day Turks.
Personally, I am not convinced either way, because I don't find it likely that a sample of modern-day Turks has much to tell us about the prehistoric relatives of the Etruscans. After all, modern-day Turks are descended from a a few dozen ancient Anatolian ethne plus a few extra-Anatolian influences from both west and east (and perhaps north and south) plus Central Asian Turkic influence minus Christian populations. We see evidence of genetic discontinuity in places with much simpler histories than Anatolia, so to claim that modern Turks have much of anything to tell us about Iron Age Etruscans is a not-so-believable proposition.
A similar complaint is that the specificity of the Etruscan gene pool can only be established by looking at their geographical neighbors. If Etruscans were intrusive to Italy, then, presumably, they would have retained differences from the surrounding Anatolian peoples.
A third (and perhaps more subtle) caveat is that "Etruscan" is polysemous. To the archaeologist and historian, it might mean a specific culture known from its remains and the texts of Romans and Greeks with which this culture interacted. To the linguist it might mean the language spoken by this culture when it attained literacy. To the geneticist it might mean the gene pool of individuals identified by archaeologists as "Etruscan".
These categories are not necessarily congruent. My favorite example is that of "Bulgarians" or "Croats", peoples who bear the name of a Turkic and Iranic people respectively, even though today they are geographically, culturally, and linguistically completely divorced from these antecedents. Or, the more controversial example of "Romans" themselves, whose nation spoke in historical times Latin, but whose histories preserved a memory of diverse origins, including, critically, an Anatolian genealogy for their eponymous ancestor.
So, the tale of Herodotus might be true (or false) on different levels. It might turn out that Etruscans did, in fact, form an isle of ancient west Anatolian genetics in Italy. Or, it might turn out that -as in the case of the Bulgarians- both language and genes are mostly native Italian, but the founding of the Etruscan nation can still be attributed to an extraneous influence. Or, perhaps Herodotus was 100% wrong, and Tyrrhenus never sailed to Italy.
Of course, I don't expect ancient DNA from all over Italy and all over Anatolia to materialize overnight, so studies such as this do help us constrain the space of possible solutions to the problem, i.e., a model with (i) substantial female participation in Etruscan colonization, (ii) genetic continuity in Anatolia to present-day Turks, and (iii) substantial contribution of Anatolian colonists to Etruscan gene pool may be falsified. But, assumptions (i-iii) describe only a small part of the space of models consistent with the Herodotean narrative.
Am J Phys Anthropol DOI: 10.1002/ajpa.22319
Genetic evidence does not support an etruscan origin in Anatolia
Francesca Tassi et al.
The debate on the origins of Etruscans, documented in central Italy between the eighth century BC and the first century AD, dates back to antiquity. Herodotus described them as a group of immigrants from Lydia, in Western Anatolia, whereas for Dionysius of Halicarnassus they were an indigenous population. Dionysius' view is shared by most modern archeologists, but the observation of similarities between the (modern) mitochondrial DNAs (mtDNAs) of Turks and Tuscans was interpreted as supporting an Anatolian origin of the Etruscans. However, ancient DNA evidence shows that only some isolates, and not the bulk of the modern Tuscan population, are genetically related to the Etruscans. In this study, we tested alternative models of Etruscan origins by Approximate Bayesian Computation methods, comparing levels of genetic diversity in the mtDNAs of modern and ancient populations with those obtained by millions of computer simulations. The results show that the observed genetic similarities between modern Tuscans and Anatolians cannot be attributed to an immigration wave from the East leading to the onset of the Etruscan culture in Italy. Genetic links between Tuscany and Anatolia do exist, but date back to a remote stage of prehistory, possibly but not necessarily to the spread of farmers during the Neolithic period.