Had the incident simply involved a DUI, Gibson could have probably gotten away with saying that he just acted irrationally. The public would have been very forgiving; actors are people, too, and people can always get too carried away with alcohol. Because Gibson tossed in those anti-semite remarks, however, his situation changed drastically. Those remarks instantly made him a target as a source of prejudice and anti-semitism. He then had to publicly apologize and admit to saying those things even in light of the previously alleged anti-semitic notions of his film "The Passion of the Christ."
The apology itself was pretty all-inclusive. He only left out his exact wording when referring to his remarks. Jewish community leaders, however, were unsatisfied. This incident required more than a simple apology, as Gibson has many more bases to cover in regards to his alleged anti-semitism than this one DUI. Of course, the apology helps his case. If he didn't apologize, some people might have been after his life. Regardless, he owes more than a public, televised statement. At this point, only further action to actually demonstrate his sincerity will convince the Jewish community he is not an anti-semite.

