I sat in on an English course at university a few years ago: ENGL242 - Digital Narrative and Digital Culture. One of the interesting points made about narrative was that there's a couple of levels to it: story and discourse, or what is told and how it is told.
When they talk about branching and funnelling in Telltale's games, that's largely about plot - the structure of the discourse. You've got a bunch of beads on a string, and they can move around a little, but the string is still there and the plot moves forward along it.
What changes, though, is the story. Your actions and dialogue choices move around the emotional tone, characterisation of the relationships between various characters, and occasionally enable or disable particular choices further down the line, but the overall structure of the story remains the same throughout.
Perhaps unsurprisingly, my Bigby is a bit softer and less of a jerk to those around him than canon. I am tempted to play through again in full "Frank Miller" mode just to see how the story changes. If I can stomach it.