There are two major possibilities here.
One, Obama was both naive and arrogant, and so he lectured the Bushies about their behaviors, even though he would have supported those actions if only he hadn't been so ignorant. In other words, Bush and Cheney were right all along, and once Obama knew what they knew, he reversed himself.
Two, Obama is an unprincipled opportunist, who played a liberal on TV when he thought that would get him votes, and happily reversed himself the moment that became the more politically convenient path.
I think it's the latter, for two reasons:
(1) There is a pattern of behavior here, of Obama moving to the politically advantageous position across a host of unrelated issues. For example, one can assume that Obama didn't suddenly discover some top-secret presidential security briefing revealing new facts about gay marriage that he was previously unaware of. Yet, nonetheless, when it was politically convenient to insist that marriage is between a man and a woman, that was his position, and then once the overall population reached an opinion tipping point where it became politically convenient to support same-sex marriage, Obama suddenly discovered a brand new principle. So, we know his character is such that he blows in the political winds.
(2) The timing of his born-again neoconservatism and presidential authoritarianism is consistent with the idea that it's dictated by politics not secret information. Think about it -- if he changed views based on receiving security briefings, we'd expect that repositioning to begin around the time when those briefings started to reach him -- probably some time after the inauguration, or, at the earliest, some time during the transition when they started to bring him up to speed. On the other hand, if he's just a spineless opportunist, we'd expect that repositioning to begin around the time he'd sewed up the Democratic nomination (when it was no longer helpful to pose as a liberal to pull the votes of the liberal base from Hillary Clinton, and instead became politically convenient to erase as much policy distance between himself and McCain as possible.) Sadly, the timing followed the latter scenario. While the Democratic nomination was still realistically in play, he was promising in no uncertain terms to filibuster the FISA vote. Then, once it was clear he'd be the nominee, he voted for the FISA amendment. This wasn't because he'd gotten some secret security briefing, long before the general election, which changed his mind. It was because he didn't want McCain to have the FISA issue to use against him, so once Clinton no longer could, he reversed himself.
I have no clue whether, as a matter of conviction, Obama was for or against the FISA changes. Was he lying to us in order to compete better against Clinton, and he actually supported the changes all along? Or was he telling the truth about his beliefs, but then voted against them as a matter of political expediency? I don't have a clue. But, whatever the case is, we clearly can't blame access to presidential security briefings for his 180-degree reversal. And since the rest of his alignment with the Bush/Cheney policy positions is just more of the same, I see little reason to think it's some secret information in those briefings driving him.
Instead, I think he's basically a scumbag who will take the path of least political resistance.... and at a time when the Republicans are cool with him killing people without trial, but would crucify him for a successful terrorist attack, the path of least political resistance is to kill anyone he remotely thinks could be a terrorist threat.