Yes, an American citizen could become a Dual Citizen of Israel and the U.S. by traveling to Israel and invoking the Law of the Return.
The issue is that once he accepts Israeli citizenship, that he thereby has dual loyalty.
I think that in the passports issued by (all?) countries, the person holding the passport swears allegiance to the issuing country. I think that the meaning of the word allegiance is such that an individual could only have allegiance to one country at a time.