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Obama is saying he doesn't want to show them because it would cause too much hatred with the Muslims etcetera, but of course killing him won't cause any hard feelings.
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Well, you can't assume all Muslims loved bin Laden and hate America... for some its the opposite. However, for those on the fence, displaying a trophy like that would definitely shove them into the "hate America" camp.
Personally, I think bin Ladens death is already confirmed even without a photo; he's obviously dead (or captured) since the greatest single embarrassment bin Laden could pull off at this time would be a video of him holding a news paper with a headline of his death, and him mocking it. If bin Laden were alive or free at this moment, there WOULD be a video or some other statement from his terrorist network refuting the story.
I don't believe 100% of the official story is true, though. The government never tells you everything. bin Laden could simply have been tired of running and gave up to the US forces, and the government created a cover story in exchange for his cooperation in exposing his terror network. Or, the government could have heard that bin Ladens died from natural causes, stormed the compound and took the body to make themselves look like the heroes.
I give the governments story a 90% chance of being what really happened. I think we might never know the what really happened, but either way, bin Laden is no longer an active participant in his network.