I think you are explaining yourself well.  You want an investigation game where the investigation is the challenge and yeah that's possible, heck I'm sure it's been done with Call of Cthulhu by some groups I've played with.  Often it ends up shifting away from the challenge though, the gm doesnt plan for failure rather he just lets the players mull around until they do solve the puzzle and find the right clue which leads to the next step.  

What you are looking for is a game where failure is an option and it has consequence.  You just have to keep that in mind when preparing (or designing) your game and in the moment.

I think it relates to a couple of the principles.

Stats are there to make the world feel real.  They are descriptors of the characters, give you a feel for what this character is like.

Advancement is there because there is no status quo in Apocalypse world.  Things are always changing, it could be stats it could be other things like a new character showing up. 

Chris:  I'm not sure I understand your example, who are the PC's in that scene and what impact did they have on what happened?