The spokesperson is correct. How on earth Palestinian action at the UN can be characterized as unilateral is Orwellian speak. Taking your case before all the nations of the world and seeking their votes is the most multi-lateral move possible. And of course, Israel is not left out at all--it has a UN vote like everyone else.
In Bahrain, 2 police officers killed, 6 wounded in bombing (AP)
from the article: Israeli intellectuals back Palestinian statehood in Tel Aviv rally