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The documentation of SDL_ActiveEvent's state member is:
"SDL_APPMOUSEFOCUS if mouse focus was gained or lost, SDL_APPINPUTFOCUS if input focus was gained or lost, or SDL_APPACTIVE if the application was iconified (gain=0) or restored(gain=1)."

The "or" leads the reader to believe that a == comparison with these constants is appropriate to detect these states, i.e. that one event is generated for each type of state change.

At least in the Windows implementation, this is not the case, though: an APPACTIVE state never comes alone, but is instead bit-or'ed together with APPMOUSEFOCUS. Code that looks like this doesn't work:

if(event.active.state == SDL_APPACTIVE) {
  active = event.active.gain != 0;
}

Either the Windows implementation is in error in that it creates mixed events (in my opinion, that is the case, as I don't think mixing events is a good idea), or the documentation is unclear or even faulty.