To proffer a tentative answer, I'm going to sketch the landscape of the comparison group -- how other presidents have been vilified.
Every president has suffered his share of invective. Some were made fun of because of their physical traits. John Adams was called "His Rotundity" and Chester Arthur was the "Walrus." Others were attacked for their character flaws. The Whigs called Jackson "King Andrew" and his successor, "Martin Van Ruin." Rutherford B. Hayes was scorned as "Rutherfraud" as a result of the Compromise of 1877. Richard Nixon was derided as "Tricky Dick" and Bill Clinton, "Slick Willie."
What is curious about the vituperation directed at Barack Obama is that the attacks are seldom directed at his body or his character. Woodrow Wilson was obsessive-compulsive, Jack Kennedy was a philandering playboy, Bush was an obstinate cowboy. Flawed characters are not ideal in our presidents, but at least we can identify with them. Most presidents are presumed American and therefore legitimate, even if they are imperfect.
Not so for Barack Obama. Many of the attacks on Obama start off with the unspoken assumption that he is so foreign and so unAmerican that he doesn't even pass the bar of legitimacy, much less identifiability. Indeed, his character may well be unimpeachable, certainly compared to Bill Clinton (pun intended). But that only reinforces his scary foreignness. Many of the attacks on Barack Obama do not even assume an identifiable personhood capable of moral corruption. He is painted as a foreigner with malign intentions on the nation when he is accused of caballing with President Medvedev, a Socialist, a Fascist, a Kenyan, or a Muslim. Whereas other presidents at least get to be Americans and identifiable persons who bear the epithets of their flaws, Obama is often cast as the secret representative of a group of marauding Others embedded amongst us.
And that is why the Obama ad claiming victory for the slaying of Osama Bin Laden was deemed by some observers as beyond the pale. The ad strikes at the heart of the insidious narrative that President Obama is unAmerican because he actually helped to take down America's greatest enemy. Yes, the ad was political. But all ads are. If it is so offensive for Barack Obama to take credit for taking out Bin Laden, maybe it is because some of Obama's critics start off from the presumption that only an American can take credit for a victory for America.
Knee-jerk reactions are often revealing. When Mitt Romney weighed in with, "any thinking American would have taken down Osama Bin Laden," he may well have unconsciously meant that his own Americanness was incontrovertible, certainly more incontrovertible than Barack Hussein Obama's. Or maybe this was a subtle pitch for the Birthers' vote. Either way, there are some Americans who simply do not think it enough to castigate Obama as a flawed American; they think it more appropriate to call out the fraudulence of an illegitimate foreigner pretending to take credit for a mission he probably wasn't even rooting for.What Mitt Romney might or might not have done about the Bin Laden raid is an open question (even if the chances of Romney not having made the same call as Obama did is near zero), even if it is not for Obama. But of course Romney has a right to be outraged. His American character is under attack.
In what world is the slaying of America's greatest enemy not grounds for credit taking, or even impolitic bragging? It is in the world inhabited by those who are convinced that Obama is not an American, and he is not for America, and so of course he cannot take credit for anything he does for America.