The 2007 study referred to in the Guardian article was carried out by the Italian geneticist Alberto Piazza et al. The study was fairly big news in 2007, and received a lot of international coverage. Another example was the article Origins of the Etruscans: Was Herodotus right?, published in the New York Times.
The 2007 study, which had the catchy title Mitochondrial DNA Variation of Modern Tuscans Supports the Near Eastern Origin of Etruscans, showed that modern populations living in three formerly Etruscan communities, exhibited a residual genetic link to communities in Turkey.
About the same time, another study, The mystery of Etruscan origins: novel clues
from Bos taurus mitochondrial DNA, had found that a local breed of cattle also shared a genetic link with Turkey.
These results were discussed in context, and in rather more depth, in the paper DNA and Etruscan Identity, by Philip Perkins of the British Museum.
One significant problem with the conclusions that we saw in much of the media in 2007 was succinctly summarised by the archaeologist Anthony Tuck:
“The architecture of the Etruscans, the language of the Etruscans — virtually every aspect of the physical and material behavior of the Etruscans — doesn't look anything like that which we see in Lydia.”
A more-recent study, Origins and Evolution of the Etruscans’ mtDNA, was carried out on the same groups but this time included mitochondrial DNA from 14 individuals buried in two Etruscan necropoleis and DNA from medieval skeletal remains. This was published in 2013.
Now, it is important to note that this study examined only maternally inherited mitochondrial DNA. However, with that caveat, this study showed no genetic link to populations in Turkey. The authors therefore concluded that their evidence strongly suggested:
... that the Etruscan culture developed locally, and not as an immediate consequence of immigration from the Eastern Mediterranean shores.
Now, as far as I know, there has been very little detailed DNA analysis on human remains from ancient Etruscan graves. Recovery of ancient DNA is difficult, and burial conditions are a significant factor in that. I am not aware of any whole-genome sequences from Etruscan remains, and the only published mitochondrial DNA sequences that I could find are those referenced in the 2013 study cited above.
So, to answer the question in your title, "Were Trojans the ancestors of the Romans?", the answer is probably not, but we don't know for certain.
As you say, there are limits to what we can infer from tests on modern populations, but there seems to be no evidence of a wholesale migration of an Eastern Mediterranean population to Tuscany.