The article in question, xposted from /r/ancientrome.
It quotes a professor and some supposed scientific evidence, but their methods honestly seem dodgy to me, such as testing the genetics of Italian residents of the last three generations - considering how many peoples have occupied both Italy and Asia Minor in the two and a half thousand years since. I'd love to hear from verifiable experts.
For those new to ancient history, the Etruscans were a group of peoples living in Etruria, a region immediately north of Rome and contemporary to its early development. Asia Minor is modern day Turkey. You can see a (limited) map of Italy here.
We can rubbish that article on the basis of its clear unprofessionalism and poor evidence. DNA testing on that level (whatever level it is, it's hardly elaborated on) would not give you any definitive conclusions. So that aside let's look at what we currently we have.
We know that the Etruscans spoke a pre-Indo-European language that belonged to the Tyrsenian language family. What this means it that Etruscans and their lingustic relatives were speaking their language in Italy (or in elsewhere in Europe) before the Italic speakers came along. Most of Europe today is Indo-European speaking, bar isolates like the Basques in Spain and the Finno-Ugrics in the east.
We only know of two other languages in the Trysenian family (that is, related to Etruscan) and those are Raetic and Lemnian. Raetic was spoken around the Alps and Lemnian was spoken on the Greek island of Lemnos (the article you linked mentions some Lemnians were tested too, this is why).
What we have then are strong links that these three languages are related, but we know nothing more about the family. The geographic spread implies a possibility that Tyrsenian languages may have been spoken all the way from Italy to the Balkans to the Aegean sea.
Now, if we look at Anatolia, we can see that the Hittites are one of the earliest attested inhabitants of Anatolia. However, they are an Indo-European speaking people and like the Italics, they too displaced pre-Indo-European speakers. These pre-Indo-European speakers in Anatolia were the Hattians, the Hurrians and the Caucasians (none of these groups are demonstrably related to each other and the Caucasians can also be split into the three further groups that are also not demonstrably related).
Although mainly restricted to Soviet linguists, there is a suggested link between Trysenian and Northeast Caucasian, which is one of these former groups. Moreover, there have been suggested relationships between both Hattian and Hurrian to Northeast Caucasian. Both the Hattians and Hurrians are presumed to originate somewhere in the lesser Caucasus or the Armenian highland, which gives more weight to these hypotheses (although the linguistic evidence is very scarce). Effectively, there is a minority view that the Tyrsenians (and therefore the Etruscans) could be from Anatolia according to these hypotheses.
Is it anything more than a hypothesis? Nope. We do not know the relationship between Northeast Caucasian and Northwest Caucasian (who still live right next to each other in the valleys of the Caucasus as they have done for thousands of years) let alone the relationship between NE Caucasian and Etruscan. Attempts to link Trysenian to any other families haven't reached mainstream linguistics at all; the languages in question are simply too thinly attested to work with.
To address the article directly, the simple matter of fact is that DNA testing does not suggest any sort of meaningful link between northern Italians and Turks, let alone Etruscans and historic Anatolians. For one there is the obvious issue of going, simply, too far back into history to get anything useful from testing modern populations. Secondly, the prevalence of the R1b Y-DNA haplogroup in Italy and Turkey is likelier the result of Indo-European migration and not pre-Indo-European relationships.
I'm reposting this from /r/archaeology for valid reasons. I can dig up more sites as needed beyond Wikipedia, but the main catalog site for Poggio Civitate seems to be down and I can't find it online just yet.
I've dug at Murlo at the Poggio Civitate field school. There's a lovely museum up in bishopry. It's a very strange site. I also didn't actually get to dig more than a week in the proper site as the Italian Forestry Service shut us down, so we ended up digging up a local Roman villa which actually turned into an Etruscan worker's domestic/work site for those who probably built Poggio Civitate.
The art is just "different" from what we would consider Roman-Mediterranean style. Many Gorgon heads (they think they were more protective than monster), male sphinxes, a statue called The Cowboy, rather complicated roofing tile matrices without anything more rudimentary in the area. Plus a lot of the local place names are just different as well. Some sound Italian, but others sound not-Italian-ish.
The genetics also go further than just human. The local cows are more related to other Turkish cows than Italian ones. Also people have been trying to do blood/DNA testing since at least the 60s when scientists were doing statistical analysis on ABO quantities in the region versus the rest of the country.
Murlo isn't exactly the best place to do genetic studies, though. It used to be the local bishopry, was shut down in the 50s-60s, and then turned into the local digging residence, then fixed up and is some pretty expensive real estate.
Vescovado (a town a couple of miles away) would be a better genetic testing location as the population is much more sedimentary and the primary families all go back several centuries (with not a lot of inbreeding to some extent). It's a fantastic town with not a whole lot to do.
http://en.wikipedia.org/wiki/Poggio_Civitate
Vescovado is the town with the orange roofing tile. Murlo is the dark squatty castle looking building (probably built over more Etruscan ruins-they loved building hill forts) to the right.
I also did a genetics paper on the Etruscans in grad school, so I'm weirdly knowledgeable in this one specific, hardcore obscure area.