More than likely, he doesn't know who his biological father his, despite his family's representations.
To your point, let's say his mother had an affair with the former baseball player Manny Mota who is from Dominican Republic. Mama Tirico found Manny irresistible while watching him against the Mets at Shea Stadium in 1965 (Little Mike T. was born in 1966).
So if in fact, we learned that Mike Tirico's biological father is actually Dominican, making him Italian and Latino,
would we still be so insistent that he claim his blackness? Probably not.