Of course not, but you don't have to overturn the act to exempt certain things from it. That's the responsibility of officials in the executive branch. For example, if certain information would reveal terrorist intelligence, but not rise to level of being classified, it could be exempted from FOIA.
Yes you are correct, there are specific exemptions in the act but the President can only restrict information consistent with and persuant to these exemptions. I’m not sure a President’s personal history falls within any of these exemptions, but then I’m not sure this type of information is even obtainable under the FOIA in the first place.