It definitely shouldn't be any wider than your bench hand placement. Personally, I keep my hands right around where they end up when I'm finishing a clean & jerk. It's almost the same hand placement as the one used when close grip benching.
I never would have even considered pressing with a false grip until I saw Wendler suggest it. The first time I used it was kind've like the first time I deadlifted sumo, I was immediately able to move more weight and I felt more comfortable doing so. I believe the biggest advantage of pressing with a false grip is that you're able to push the bar back behind your head more, so the bar ends up traveling in a straight line as it's supposed to.