"I think what the author is saying is that had the US sought and obtained the support of Middle Eastern countries in removing Saddam then he would have supported even an illegal invasion."

Well, first the US is not going to do an illegal invasion. We are a country that is ruled by law.
Second, of course, the US obtained support of Middle Eastern countries. If fact, what's remarkable and the amount of support we got from Iran- they publically declared they would be neutral; considering our poor relations with this country that was quite remarkable.

Of course we couldn't wish for any more support than what we received from Kuwait. Saudi Arabia and Jordan were very supportive.
In general the arab countries provided more support than one of our oldest ally, France.