The first mistake anyone who flings the “anti-American” accusation makes is to equate the government with the society as a whole. If someone or something is critical of the U.S. government, it is very often deemed anti-American or, if the person doing the criticising is American, unpatriotic. This plays by the state’s rules: it makes patriotism dedication to the state, rather than the country, and it makes the state into the embodiment of America. This is simply not true, and it’s a very good thing at times that this isn’t true. That doesn’t mean that the citizens don’t have some small part to play in the dreadful policy decisions made by the state (it is our government, after all), but the decisions being taken in Ultimatum are the sort that the public is never supposed to know about because the average citizen of this country would still probably be horrified at ordering the deaths of foreign journalists in the name of protecting some part of the behemoth security state.
Okay, but let's not take this too far. For instance, I would submit that a film like Braveheart (which, like the Bourne movies, I'm very fond of) qualifies as obviously "anti-English" even though it's technically only critical of the English government and military, or that the infamous Valley of the Wolves is an anti-American movie even though it mainly concerns itself with the wickedness of certain American soldiers (and evil Jewish-American doctors, of course). Obviously, the phrase "anti-American" is at once loaded and nebulous, but I think that it's fair to say that any film that leaves the audience with an overwhelmingly and cartoonishly negative impression of a particular nation qualifies as "anti" that nationality, whether that impression is primarily formed through a representation of that nation's government or not. I take Daniel's point, and Chris's, that the Joan Allen-Julia Stiles axis may offer enough of an alternative vision of what an American is to get The Bourne Ultimatum off the hook in this regard, but I think it definitely tiptoes toward anti-American territory more than its predecessors, by being more cartoonish in its depiction of the pervasiveness - as opposed to just the presence - of naked, self-aware evil within the U.S. bureaucracy.