"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.....
Donald Trump: Israeli settlement construction in West Bank should 'keep going' (Haaretz)
from the article: A new party of good tidings