You can't explain this without giving away the whole thing, so... spoilers ahead.
I was going to cover this in my Part 2 of my Action Comics #900 review, but it seems the media is going coo-coo over this one.
No doubt, DC could have been handled better, but its also the sort of thing that you kind of have to expect will be taken absolutely the wrong way as certain parties re-purpose the one panel for their own means. And that's too bad.
The upshot is that Superman realizes that he can't actually act on a global scale without being seen as an agent of the US government intruding on foreign soil. In 2011, with a readership no longer comprised mostly of 13 year-olds with a mystical belief that America = Magic, this move actually makes more sense than Superman just buzzing into any airspace he likes and with no expectation of an international incident bubbling up (by the way, they have played up the "international incident caused by Superman's appearance" angle on numerous occasions).
The story is basically: Superman hears that there are pro-democracy protests going on in Tehran, so he hops over to Iran and stands with the protestors (literally stands and takes no action as any action could go wrong or be taken as the start of hostilities). For anyone actually reading the paper in our world, unsurprisingly the Iranian government of Superman's world declares Superman's appearance to be undue meddling from the West, and the visit causes an international incident.
With a mix of satisfaction that he did achieve his goal of supporting pro-democracy protesters and concern regarding how his appearance is being used on the international stage, Superman comes to an unhappy decision regarding his stated citizenship.
Mindful of what he thinks he should be doing versus what he thinks will happen if he did this again, he has to tell the US Government "look, you guys are great, but I'm not going to be responsible for starting a war and I need to help people all over this rock you call Earth." Its not about turning one's back on America, its about a modicum of self-awareness when one is a super-being who sneezes off nuclear weapons.
I've been asked before it bothers me that in Superman Returns the only mention of Truth, Justice and the American Way was shortened to "Truth... Justice... All that stuff". And I've always said that it doesn't really bother me one way or another. The entire catchphrase was added during a particularly jingoistic era, and when you consider Superman as a globe-trotting, occasionally space-faring alien for whom borders and local politics are at best an inconvenience, I think it makes sense he likes the American Way, but he can't necessarily be as efficient as possible if he's having to show his Visa every time he crosses a border.
And so this is a bit different from dropping The American Way from the Superman's motto. While I get what people decide they want to say "The American Way" means (and they aren't necessarily wrong*), that's not what the story is talking about. Its about whether or not rolling a nuclear missile draped in the Stars and Stripes into Tienanmen Square is or is not going to cause the US some political grief. Or, in fact, if Superman need really be beholden to the US State Department or any US service.
Mostly, I don't think DC was wrong to define Superman's citizenship, or a lack thereof. It wasn't a slam on the US or US policy. By even trying to answer the question, in a lot of ways, the 9 page story was a bit of fan-wank. These are the sorts of questions that keep comic geeks awake at night. "If there was a catastrophe in North Korea, would Superman risk war between the US and North Korea to go in and help people? Should he be beholden to Homeland Security travel warnings?" That's the question the Superman of the story was addressing. Frankly, its the sort of anarchic thing Superman might have done in his earliest, most-free-wheeling days when we didn't think of Superman as Dad/ The World's Oldest Boyscout and/ or the writers weren't worried about being called on the mat by Estes Kefauver trying to drum up some political drama.
I am guessing, however, that certain outlets are having kittens today about a couple of panels in a Superman comic. Which is kind of hilarious. Their beloved Superhero (whose comic, I assure you, they will not have read) has turned his back on America!
By the way, these sorts of little homily stories show up all the time as filler in issues with extended page counts. Likely, the story won't get mentioned again anywhere else. And, no, I didn't think that the story was particularly necessary, and if they were going to do it, it could have been handled much, much better.
Funny thing is: I think if you heard Batman didn't recognize borders in his quest for justice, you'd say "right on, man. That guy is a BADASS. Rock'n'roll!" Little harder to do that with Superman (one of his co-creators, by the way, was Canadian, so chew on that for a while).
*we can discuss whether the US has a divine destiny or is particularly magically blessed some other time