"Israeli-Arab" refers to Israelis who are Arab. Just like you point out that "Jew" and "Arab" are not opposing terms, neither are "Israeli" and "Arab". Your suggestion is actually far worse than Burg's suggestion (which actually makes sense), because you're automatically disqualifying Arabs from also being Israeli.....
AG examines probes deal by new police chief Hirsch's security firm (Haaretz)
from the article: A new party of good tidings