Historically that's the best guess we have. Or did you think a rando guy from Bethlehem looked any different than the rest of the Mediterranean? What you should indeed question though is blonde hairs and blue eyes, that's quite unlikely (though not unheard of).

"Caucasian" now that's more questionable the term in itself is bunk and the stuff that backed it up back then is now understood to be the archaeological evidence of the spread of the Indo-European languages out of their Urheimat (ballpark Ukraine/Caucasus). But you'll have a hard time telling a Sicilian, Greek, Turk, Palestinian, or say Tunisian apart because guess what, the sea is a highway, people fucked.

Or are you one of those Seppos who think Egyptians are black?