I don't have the immunology expertise to analyze this particular study (e.g. in re cross-reactivity), but I'll just note when it come to antibodies, results are harder to interpret than for PCR tests, e.g.
Two preliminary retrospective studies in the United Kingdom, sub-Sahara Africa, and the United States suggest that some people who were never infected with the virus that causes COVID-19 have cross-reactive antibodies against it—perhaps from previous exposure to similar human coronaviruses.
[...]
the researchers analyzed more than 300 blood samples collected from 2011 to 2018. While almost all samples had antibodies against coronaviruses that cause the common cold, 16 of 302 adults (5.3%) had antibodies that would recognize SARS-CoV-2—regardless of whether they had recently had a cold
In bit further detail, that study (in Science) found that some S2-specific antibodies that neutralize SARS-CoV-2 also neutralize the common-cold coronaviruses, which is basically their explanation for this cross-reactivity.
I'll note though that the Italian study used a sample of convenience:
individuals enrolled in a prospective lung cancer screening trial between September 2019 and March 2020
Who knows what they may have found if e.g. their sample extended back to 2018 or to 2011 as other studies on antibodies have done.
Also the Italian (Turmori) study only has one citation in another paper (also from Italy) insofar, so I can't find much in the way of expert commentary on it. (If you're curious, the paper citing it is on "Unexpected volume of Google Searches for COVID-19 symptoms in the prepandemic period in Lombardia, Italy")
Now on the angle obscure papers on this matter, there's one which concluded (on similar immunology arguments) that the virus had been circulating in Brazil since February 2019 (not a typo). I wasn't able to find 3rd party commentary on this study either.
Of some interest however, both the Brazil and Italy studies only looked at IgG and IgM, but another Dec 2020 study in Science found that an IgA spike is the best indicator of a recent SARS-CoV-2 infection. In other words, beside possible cross-reactivity issues, both the Brazil and Italy studies seem to have poor time-specificity as to when a putative infection had happened, prior to the detection of the antibodies (they measured).
