Oh good grief. I like a good conspiracy theory, but this isn’t one of them.
The current theorists suppose that the Republicans and their various opposition research teams are completely incompetent. I think we can depend on them for stuff like this: they may have trouble winning elections lately, but I’m sure their dirt-digging skills are undiminished.
You can bet that if there was a shred of doubt about Obama’s citizenship it would have been raised early on in the presidential campaign.