της καλουμενης ιταλικης
Same adjective. That there was no political entity "Italy" has nothing to do with the use of the word in either the article's context or the New Testament's
Nor is there a different adjective in the modern everyday use. Google for example, "ιταλικη κουζίνα".
The New Testament’s use of Italic is to describe a pagan centurion NOT a follower of Chrstian or a Christian saint.
Once the peninsula was Chrstianized the term Italian or Italic makes no sense.
Words generally have shades of meaning, and if one is to read carefully, one must put them into historical context. Identical spelling of an adjective does not mean that its use in two widely distinct contexts may be presumed to be identical. “Virginian” in 1763 would be related to yet distinct from the same term in 1784 or in 1820 or in 1863 or in 1963. The 19th century unification of the Italian peninsula is responsible for the common modern notion of what Italian means, which is related to yet not identical with past usages. At the time of St. Rosa’s death, Italian identity would be minimal—most of the wars that the governments on the peninsula were involved with were with each other, or at least against each other as parts of complex alliances.
The BBC guy is being sloppy, but given the level of education that his readers have, it is easiest to perpetuate the fiction that the present social/political units have largely existed from time immemorial.